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Find the coordinates of foot of perpendicular from the point (2,3) to the line 3x+4y+8=0.
Q.17 of miscellaneous ex. of N cert book chapter 10 st. line
The base of the equilateral triangle has an equation of x+2y=3 and one of the vertex is (1,1).find the equation of other two sides
the point P is the foot of the perpendicular from A(0,t) to the line whose equation is y=tx. Determine
a) the equation of line AP
b) the co-ordinate of P
c) the area of triangle OAP, where O is origin
the equation of the perpendicular bisectors of sides AB and AC of a triangle ABC are x-y+5=0 and x+2y=0respectively. if the point is A (1,-2), find the equation of line BC.
Find the equation of the circle which passes through the points P(1,0), Q(3,0) and R(0,2). Find also (i) The coordinates of the other point in which the axis of y cuts the circle, (ii) The coordinates of the other end of diameter through Q.
Two adjacent sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0.If the equation of one of the diagonals is 11x + 7y = 4, find the equationof the other diagonal.
A line is such that it's segment between the lines 5x-y+4=0 and 3x+4y-4=0 is bisected at the point (1,5) obtain it's equation?
sir, can u explain me how to find tan inverse in log books..
find the coordinates of the incentre and centroid of the triangle whose sides have the equation 3x -4y=0, 12y+5x=0, y-15=0.
also please tell me what is incentre, circumcentre, orthocentre and centroid in a triangle
Find the equation of straight line whose intercepts on the axes are thrice as
two sides of an isocesle triangle are given by the equation 7x-y+3=0 and x+y-3=0. if its third side passes through the point (1,-10) then its equations are-
The hypotenuse of a right angled triangle has its ends at points (1,3) and (-4,1).Find the equation of the legs (perpendicular sides) of the triangle.
Find the image of the point (1,2) in the line x-3y+4 =0
Find the equations of the lines which pass through (4,5) and make equal angles with lines 5x-12y +6 =0 and 3x-4y-7=0
the distance of the point (3,5) from the line 2x +3y - 14 = 0 measured parallel to the line x - 2y = 1 is ?
a) 7/ root 5
b) 7/ root 13
c) root 5
d) root 13
NCERT - miscellaneous exercise ch 10 Q-17
The end points of the hypotenuse of a right angled triangle are (1,3) and (-4,1). Find the equation of the legs of the triangle.
Show that the points A(7,10), B(-2,5) and C(3,-4) are the vertices of an isoceles right-angled triangle.
The area of the triangle formed by the coordinate axes and a line is 6 square units and the length of the hypotenuse is 5 units . Find the equation of the line
find the equation of the line through the intersection of the lines 2x+3y-4 = 0 and x-5y = 7 that has its intercept equal to -4.
Find the point on the line x+y+9=0 whose distance from the line x+3y-8=0 is3√10 units.
if A(1,4) B(2,-3) C(-1,-2) are the vertices of a triangle ABC. find
a) the equation of the median through A
b) the equation of altitude through B
c) the right bisector of BC
A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.
Find the equation of the circle passing through the points (1,2), (3,-4) and (5,-6)
1. find the equation of perpendicular bisectors of the line segment joining the points (1,1) and (2,3)
2. Find the eq of the line which passes through the points (3,4) and the sum of its intercepts on the axes 14
Find the orthocentre of the triangle the equation of whose sides are x+y=1, 2x+3y=6, 4x-y+4=0
One side of a rectangle lies along the line 4x + 7y + 5 = 0. Two of itsvertices are (–3, 1) and (1,1). Find the equation of other three sides.
if the image of the point(2,1) with respect to a line mirror be (5,2), find the equation of the mirror.
find the equation to the straight line which passes through the point of intersection of the line 3x+4y-1=0 and 5x+8y-3=0 and is perpendicular to the line 4x-2y+3=0
Consider a family of straight lines (x + y) + lambda(2x - y + 1) = 0. Find the equation of the straight line belonging to this family that is farthest from (1, -3).
Kindly please don't refer me the link to a similar question that ha s already been answered as I tried that method but I got a wrong answer.
Thank You.
Find the eq. of the straight lines which go through the origin and trisect the portion of the straight line 3x+y=12 which is intetercepted between the axes of the coordinates.
the lones x-2y+6=0 and 2x-y-10+0 intersect at P.Without finding the coordinates of prove that the equation of the line through P and the origin of coordinates is perpendicular to 39x+33y-580=0.
the diagonal of a square lies along the line 8x-15y=0 one vertex is (1,2). find equations to the side of square passing through it?
Find equation of medians of triangle ABC whose vertices are A(2.5) B(-4,9) C (-2,-1)
Find the equation of bisector of angle A of triangle whose vertices are A(4,3) , B(0,0) & C(2,3)
How to split a pair of line equation of ax2+2hxy+by2+2gx+2fy+c=0 in the short method?
Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
what difference it will get when it become clockwise in place of aticlockwise.
find the equation of the straight line which cuts off intercepts on x axis twice that on y axis and is at a unit distance from the origin
find the distance of the point (2,3) from the line 2x-3y+9=0 measured along a line making an angle of 45degreewith the x axis
find what the following equation becomes when the origin is shifted to the point(1,1)
x2+xy-3y2-y+2=0
triangle is formed by joning three lines x+y-6=0,3y-x+2=0 and 3y=5x+2?find the orthocenter of the triangle?
if G is the centroid and I the incentre of the triangle with vertices A(-36,7) ,B(20,7) ,C(0,6) then find the value of GI?
Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.
Find the equation of a straight line which passes through the point (1,-3) and makes an intercept on y-axis twice as long as on x-axis
find the equation of passing through the point (3,2) and whose slope is 3/4. find the coordinates of the points on the same line that are 5 units away from the point (3,2)
If the co-ordinates of a variable point P be (acostheta,bsintheta) where theta is a variable quantity, find the locus of P.
find the distance of the point [3,2] from the straight line whose slope is 5 and is passing through the point of intersection of lines x+2y=5and x-3y+5=o
If p and q are the lengths of perpendiculars from the origin to the lines x cos θ – y sin θ = k cos 2θ and x sec θ+ y cosec θ = k, respectively, prove that p2 + 4q2 = k2
a straight line makes an intercept on the y axis twice as long as that on the x axis and is at a unit distance from the origin.determine its equation (pls slove it)
Find the equation of a line on which perpendicular from the origin makes an angle of 30 degree with the x-axis and which forma a triangle of area 50/3^1/2 with the coordinate axes ?
Find the equation of the line through the intersection of lines 3x + 4y = 7 and x – y + 2 = 0 and
Find the equation of a line passing through (1, 2) and making angle of 300 with y-axis.
If a vertex, the , circumcenter, and the centroid of a triangle are ( 0, 0 ), (3, 4) and (6, 8) respectively, then the triangle must be a. a right angles triangle b. an equilateral triangle c. an isosceles triangle d. a right-angled isosceles triangle Sol: Clearly, ( 0, 0 ), (3, 4) and (6, 8) are collinear. So, the circumcenter M and the centroid G are on the median which is also the perpendicular bisector of the side. So the triangle must be isosceles. How did we come to know they're on the median and also the perpendicular bisector? (I couldn't understand it through the triangle I plotted. Please make a figure if that makes things easier)
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Syllabus
Find the coordinates of foot of perpendicular from the point (2,3) to the line 3x+4y+8=0.
Q.17 of miscellaneous ex. of N cert book chapter 10 st. line
The base of the equilateral triangle has an equation of x+2y=3 and one of the vertex is (1,1).find the equation of other two sides
the point P is the foot of the perpendicular from A(0,t) to the line whose equation is y=tx. Determine
a) the equation of line AP
b) the co-ordinate of P
c) the area of triangle OAP, where O is origin
the equation of the perpendicular bisectors of sides AB and AC of a triangle ABC are x-y+5=0 and x+2y=0respectively. if the point is A (1,-2), find the equation of line BC.
Find the equation of the circle which passes through the points P(1,0), Q(3,0) and R(0,2). Find also
(i) The coordinates of the other point in which the axis of y cuts the circle,
(ii) The coordinates of the other end of diameter through Q.
Two adjacent sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0.
If the equation of one of the diagonals is 11x + 7y = 4, find the equation
of the other diagonal.
A line is such that it's segment between the lines 5x-y+4=0 and 3x+4y-4=0 is bisected at the point (1,5) obtain it's equation?
Thank You.
sir, can u explain me how to find tan inverse in log books..
find the coordinates of the incentre and centroid of the triangle whose sides have the equation 3x -4y=0, 12y+5x=0, y-15=0.
also please tell me what is incentre, circumcentre, orthocentre and centroid in a triangle
Find the equation of straight line whose intercepts on the axes are thrice as
two sides of an isocesle triangle are given by the equation 7x-y+3=0 and x+y-3=0. if its third side passes through the point (1,-10) then its equations are-
i) touches the X axis
ii) lies entirely inside the circle x^2 + +y^ = 18
The hypotenuse of a right angled triangle has its ends at points (1,3) and (-4,1).Find the equation of the legs (perpendicular sides) of the triangle.
Find the image of the point (1,2) in the line x-3y+4 =0
Find the equations of the lines which pass through (4,5) and make equal angles with lines 5x-12y +6 =0 and 3x-4y-7=0
the distance of the point (3,5) from the line 2x +3y - 14 = 0 measured parallel to the line x - 2y = 1 is ?
a) 7/ root 5
b) 7/ root 13
c) root 5
d) root 13
NCERT - miscellaneous exercise ch 10 Q-17
The end points of the hypotenuse of a right angled triangle are (1,3) and (-4,1). Find the equation of the legs of the triangle.
Show that the points A(7,10), B(-2,5) and C(3,-4) are the vertices of an isoceles right-angled triangle.
are at right angles. Also find the equation to the diagonals of the parallelogram.
The area of the triangle formed by the coordinate axes and a line is 6 square units and the length of the hypotenuse is 5 units . Find the equation of the line
find the equation of the line through the intersection of the lines 2x+3y-4 = 0 and x-5y = 7 that has its intercept equal to -4.
Find the point on the line x+y+9=0 whose distance from the line x+3y-8=0 is3√10 units.
if A(1,4) B(2,-3) C(-1,-2) are the vertices of a triangle ABC. find
a) the equation of the median through A
b) the equation of altitude through B
c) the right bisector of BC
A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.
Q. Line x/6 +y/8 =1 intersects the x and y axes at M and N respectively. If the coordinates of the point P lying inside the triangle OMN (where 'O' is origin) are (a, b) such that the areas of the triangle POM, PON and PMN are equal. Find
(a) the-coordinates of the point P and
(b) the radius of the circle escribed opposite to the angle N.
Find the equation of the circle passing through the points (1,2), (3,-4) and (5,-6)
1. find the equation of perpendicular bisectors of the line segment joining the points (1,1) and (2,3)
2. Find the eq of the line which passes through the points (3,4) and the sum of its intercepts on the axes 14
~~The sides of a triangle are given by the equation 3x+4y=10,4x-3y=5, and 7x+y+10=0. Show that the origin lies within the triangle.
Find the orthocentre of the triangle the equation of whose sides are x+y=1, 2x+3y=6, 4x-y+4=0
One side of a rectangle lies along the line 4x + 7y + 5 = 0. Two of its
vertices are (–3, 1) and (1,1). Find the equation of other three sides.
Paragraph for Question 12 to 14
Let B13x + 4y – 10 = 0 and B2 4x – 3y – 5 = 0 are bisectors of angle between lines L1= 0 and L2 = 0. If L1 passes through origin and L2 = 0 meets the curve y2 = 4ax at A and B.
On the basis of above information answer the following :
Q12. Equation of line L1 = 0 is –
(A) x = 2y (B) y = 2x (C) x + y = 2 (D) x – y = 4
Q13. Equation of line L2 = 0 is –
(A) 11x + 2y = 24 (B) 11x – 2y = 20 (C) 5x + 3y = 13 (D) 3x + 5y = 10
Q14. If AB subtends 90° at origin then a is equal to -
Ans (5,6) or(3,4)
if the image of the point(2,1) with respect to a line mirror be (5,2), find the equation of the mirror.
find the equation to the straight line which passes through the point of intersection of the line 3x+4y-1=0 and 5x+8y-3=0 and is perpendicular to the line 4x-2y+3=0
Consider a family of straight lines (x + y) + lambda(2x - y + 1) = 0. Find the equation of the straight line belonging to this family that is farthest from (1, -3).
Kindly please don't refer me the link to a similar question that ha s already been answered as I tried that method but I got a wrong answer.
Thank You.
Find the eq. of the straight lines which go through the origin and trisect the portion of the straight line 3x+y=12 which is intetercepted between the axes of the coordinates.
the lones x-2y+6=0 and 2x-y-10+0 intersect at P.Without finding the coordinates of prove that the equation of the line through P and the origin of coordinates is perpendicular to 39x+33y-580=0.
the diagonal of a square lies along the line 8x-15y=0 one vertex is (1,2). find equations to the side of square passing through it?
Find equation of medians of triangle ABC whose vertices are A(2.5) B(-4,9) C (-2,-1)
Find the equation of bisector of angle A of triangle whose vertices are A(4,3) , B(0,0) & C(2,3)
How to split a pair of line equation of ax2+2hxy+by2+2gx+2fy+c=0 in the short method?
Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
what difference it will get when it become clockwise in place of aticlockwise.
find the equation of the straight line which cuts off intercepts on x axis twice that on y axis and is at a unit distance from the origin
find the distance of the point (2,3) from the line 2x-3y+9=0 measured along a line making an angle of 45degreewith the x axis
find what the following equation becomes when the origin is shifted to the point(1,1)
x2+xy-3y2-y+2=0
triangle is formed by joning three lines x+y-6=0,3y-x+2=0 and 3y=5x+2?find the orthocenter of the triangle?
if G is the centroid and I the incentre of the triangle with vertices A(-36,7) ,B(20,7) ,C(0,6) then find the value of GI?
Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.
Find the equation of a straight line which passes through the point (1,-3) and makes an intercept on y-axis twice as long as on x-axis
find the equation of passing through the point (3,2) and whose slope is 3/4. find the coordinates of the points on the same line that are 5 units away from the point (3,2)
If the co-ordinates of a variable point P be (acostheta,bsintheta) where theta is a variable quantity, find the locus of P.
find the distance of the point [3,2] from the straight line whose slope is 5 and is passing through the point of intersection of lines x+2y=5and x-3y+5=o
If p and q are the lengths of perpendiculars from the origin to the lines x cos θ – y sin θ = k cos 2θ and x sec θ+ y cosec θ = k, respectively, prove that p2 + 4q2 = k2
(i) ITS INTERCEPTS ON THE AXES (ANS IN THE TB : 3, -3/2)
(ii) THE LENGTH OF THE PORTION OF THE LINE INTERCEPTED BETWEEN THE AXES (ANS IN TB: 3√5/2)
(iii) THE SLOPE OF LINE ( ANS IN TB: 1/2)
a straight line makes an intercept on the y axis twice as long as that on the x axis and is at a unit distance from the origin.determine its equation (pls slove it)
Find the equation of a line on which perpendicular from the origin makes an angle of 30 degree with the x-axis and which forma a triangle of area 50/3^1/2 with the coordinate axes ?
Find the equation of the line through the intersection of lines 3x + 4y = 7 and x – y + 2 = 0 and
Find the equation of a line passing through (1, 2) and making angle of 300 with y-axis.
If a vertex, the , circumcenter, and the centroid of a triangle are ( 0, 0 ), (3, 4) and (6, 8) respectively, then the triangle must be
a. a right angles triangle
b. an equilateral triangle
c. an isosceles triangle
d. a right-angled isosceles triangle
Sol: Clearly, ( 0, 0 ), (3, 4) and (6, 8) are collinear. So, the circumcenter M and the centroid G are on the median which is also the perpendicular bisector of the side. So the triangle must be isosceles.
How did we come to know they're on the median and also the perpendicular bisector? (I couldn't understand it through the triangle I plotted. Please make a figure if that makes things easier)