if(-4,3)and(4,3)are two vertices of an equilateral triangle. find the coordinates of the third vertex. given that the origin lies in the interior of the triangle.

How to prove three points collinear by Section Formula

Q1=Two opposite  vertices  of a square  are (-1,2)and (3,2).Find the coordinates of other two vertices.

Q2=If two opposite vertices  of a square of  a square are (5,4)and (1,-6) ,find the coordinates of its remaining two vertices.

THE VERTICES OF TRIANGLE ABC ARE A(4,6) , B(1,5) , C(7,2). A LINE  IS DRAWN TO INTERSECT SIDES AB AND AC AT D AND E RESPECTIVELY SUCH THAT AD/AB=AE/AC=1/4. CALCULATE THE AREA OF TRIANGLE ADE AND COMPARE IT WITH AREA OF TRANGLE ABC.

 if p(x,y ) is any point on the line segment joining the points A(a , 0) and B(0,b) then show that x/a + y/b = 1

xam idea model paper - 1 (unsolved-1)

Determine the ratio in which the line 2x+y-4=0 divides the line segment joining point A(2,-2) & B(3,7)?

Find the centre of a circle passing through the points (6,-6), (3,7) and (3,3).

Please clarify this doubt :

QUESTION :

FIND THE POINT ON THE X AXIS WHICH IS EQUIDISTANT FROM ( 2,-5) AND ( -2, 9 )

DOUBT :

THIS PROBLEM WHEN SOLVED CONSIDERING THE TWO PINTS GIVEN GIVEN AS P AND Q AND THE MID POINT AS R , WE GET PR = QR AND WE GET RESULT AS R = ( -7, 0 )

WHY DOES THE SECTION FORMULA REDUCED TO EQUIDISTANT FORMULA  ( X1 + X2 )/ 2  SINCE M1 = M2  DOES NOT GIVE SAME ANSWER .

SO IS THE EQUIDISTANT FORMULA NOT VALID TO BE USED WHEN THE INTERSECTION IN ON THE AXIS ( X AXIS OR Y AXIS ).

THE SAME EQUIDISTANT FORMULA WORKS IN OTHER CASES, FOR EXAMPLE IN THE BELO W QUSETION ( TRISECTION ).

FIND THE COORDINATES OF THE POINTS OF TRISECTION OF THE LINE SEGMENT JOINING POINTS A( 2,-2), B(-7,4 ).

PLEASE CLARIFY IMMEDIATELY.

THANKS

1. rs aggarwal question and ans of class 11 ch sequence serise

Find the value of 'p' for which the points (-1,3) , (2,p) and (5,-1) are collinear.

the distance between 2x+4=0 and x-5=0 is ?

Find the ratio in which the line 3x + y - 9 = 0 divides the line segment joining the points A(1,3) and B(2,7)

the mid points of the sides of a triangle are (3,4) , (4,1) , (2,0).find the coordinates of the vertices of the triangle.

IF P and Q are two points whose coordinates are ( at^2,,2at) and ( a/t² , - 2a/t) respectively and S is the point ( a,0).. Show that 1/SP + 1/SQ is independent of t

In what ratio the line segment joining the points (-2,-3) and (3,7) is divided by the y – axis ? Also, find the co – ordinates of the point of division

 let the opposite angular points of a square ABCD be  A(3,4) C(1,-1).find C and D

 find the coordinates of the point equidistant from three given points A (5 , 1 ) , B (-3,-7 ) and C( 7, -1).

If the points A (1,-2) B (2,3)C (-3,2) D (-4,-3) are the vretices of parallelogram ABCD, then taking AB as the base find the height of the parallelogram

 If G be the centroid of a triangle ABC, prove that,  AB²+BC²+CA²=3(GA²+GB²+GC²)

If A(1,2) , B(4,3 ) and C( 6,6) are the three vertices of a parallelogram ABCD , find the coordinates of the fourth vertex D

Find a relation between x and y such that the point P(x,y) is equidistant from the points A(7,1) and B(3,5) .

The age of the father is twice the sum of the ages of his two children.After,20 years , his age will be equal to the sum of the ages of his children.Find the age of the father

Two Vertices of a triangle ABC are given by A(6,4) and B(-2,2), and its centroid is G(3,4). Find coordinates of the third vertex C of Triangle ABC.

Q1) Prove that the points (a,0),(b,0), and (1,1) are collinear if 1/a + 1/b =1

Q2) Prove that the points (a,b), (c,d), and ( a-c,b-a) are collinear if ad=bc.

Q3) three consecutive vertices of a parallelogram ABCD are A (1,2) B (1,0) and C (4,0).Find the fourth vertex.

Find the coordinates of a point whose distance from (3,5) is 5 units and that from (0,1) is 10 units..

Four points A(6,3) , B(-3,5) , C(4,-2) , and D(x,3x) are given in such a way that

area of triangle DBC/area of triangle ABC =1/2. Find x

1. the line segment joining the points (3,-4)and (1,2)is trisected at the points Pand Q. if the coordinates of Pand Q are (p,-2) and (5/3,q) respectively, find the values of p and q .

if a(2,2) ,b(-4,4) c(5,-8) are the vertices of a triangle, then find the lenght of median through vertex c?

in what ratio does the x-axis divide the segment joining the points (-4,-6) and (-1,7), also find the coordinates of point of division

find the circumcentre of the triangle whose vertices are (-2,-3), (-1,0), (7,-6)

A(6,1), B(8,2), C(9,4) are three vertices of a parallelogram ACBD. If E is midpoint of DC, find the area of ∆ADE.

Find the point on Y-axis which is equidistant from the points (5,-2) and (-3,2)?

The base BC of an equilateral triangle ABC lies on y axis. The coordinates of pt. C are (0,-3). If the origin is the mid pt. of the base BC, find the coordinates of the pt. A and B and hance find the area of the triangle.

Find the area of the quadrilateral whose vertices taken in order are (-4, -2), (-3, -5 ), (3, -2), and (2,3)........

If the midpoints of sides of the triangle PQR are (1,2) (0,1) (1,0), then find the cordinates of thevertices of the triangle.

find the ratio in which the line 2x + 3y - 5 = 0 divideds the line segment joining the points (8,-9) and (2,1) . also find the coordinates of the point of division.

 the line segment joining the points A ( 2 , 1 )  B ( 5 , -8 ) is trisected at the points p and q such that P is nearer to A . if P also lies on the line given by 2 x - y + k =0 , find the value of k. 

If R( x , y ) is a point on the line segment joining the points P( a , b ) and Q( b , a ) , then prove that x+y =a+b

If the point (x,y) is equidistant from the points (2p +q,2q - p) and (2p - q,p + 2q), prove that qx = py.

FIND THE RATIO IN WHICH THE Y- AXIS DIVIDES THE LINE SEGMENT JOINING THE POINTS ( 5 , -6 ) AND ( -1 , -4 ) .

for such a question i know that the ratio is taken as k : 1 . But what ratio should be taken if it is asked for x - axis ?

Is it the same ?

1. In a circle of radius 21cm, an arc subtends an angle 60 degree at the centre. Find

(i) the length of the arc  (ii) area of the sector formed by the arc

  (iii)area of the line segment formed by the corresponding chord.

find the ratio in which point P(-1,y) lying on the line segment joining points A(-3,10) and B(6,-8) divides it. also find the value of y.

The point R divides the line segment AB, where A (-4,0) and B (0,6) are such that AR=3/4AB. Find the coordinates of R.

Find the area of the Quadrilateral ABCD whose vertices are A ( -3 , -1) , B (-2, -4) , C ( 4, -1) andD (3,4) . ..

Find the point on x-axis which is equidistant from the points (2,-5) and (-2,9)

prove that the points (0,0), (5,5), (-5,5) are the vertices of a right angled triangle.

if the points A(4,3) and B(x,5) are on the circle with centre O(2,3), find the value of x.

1. two vertices of a triangle are (1,2), (3,5), and the centeroid is at the origin. Find the third vertex.
2. Find the coordinates (x,y) of a point whose distance from points (3,5) is 5 units & that from (0,1) is 10 units , given that 3x=2y
3. If 3b is the length of a side of an equilateral triangle ABC ,base BC lies on x-axis & B lies of origin , find the coordinate of vertices of ABC 

Find a point on y axis which is equidistant from the pts. A(6,5) and B(-4,3).

1- the perpendicular bisector of line segment joining the points a(1,5) b(4,6) cuts y axis at which point

2-if the point p (2,1)lies on the line segment joining points a(4,2 ) and b (8,4) then

a- ap=1/3ab , b- ap=pb, c- pb=1/3ab d- ap=1/2 ab choose the correct option

i m getting the relation ab=4 ab am i right or wrong plz specify this

3- show that a (-3,-1), b- (-4,-1), c(3,3) , d (4,3) r the vertices of rhombus i m not getting rhombus

In what ratio does the y-axis divide the line segment joining the points (-4,5) and (3,-7).

 IN WHAT RATIO DOES THE LINE x-y-2=0 divide the line segment joining (3,-1) and (8,9) ?

Find the coordinates of the cicumcentre of the triangle whose vertices are (8,6), (8,-2) and (2,-2). Also find its circumradius.

(plz explain step wise)

find the area of a triangle ABC whose vertices are A(1,-1) B(-4,6) and (-3,-5)

Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, − 1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

The coordinate of two points A and B are (3,4) and (5,-2) respectively. Find the coordinate of point P if PA=PB. The area of triangle APB=10.

Find the value of k if the points A(k+1, 2k), B(3k, 2k+3)and C (5k – 1, 5k) are collinear.

If two opposite vertices of a square are (5,4) and (1,-6), find the co ordinates of its remaining two vertices.