find the equation of passing through the point (3,2) and whose slope is 3/4 find the coordinates of the - Maths - Straight Lines

Question

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)

Ajanta Trivedi · Accepted Answer

equation of a line which passes through the point $(x_{1}, y_{1})$ and has slope m is given by:

$y - y_{1} = m (x - x_{1})$ .........(1)

thus the equation of a line which passes through the point (3, 2) and slope = 3/4 is:

$y - 2 = \frac{3}{4} (x - 3) 4 (y - 2) = 3 (x - 3) 4 y - 8 = 3 x - 9 3 x - 4 y = 9 - 8 3 x - 4 y = 1$ ............(2)

slope = 3/4

$\tan θ = \frac{3}{4} \Rightarrow \sin θ = \frac{3}{5} a n d \cos θ = \frac{4}{5}$

equation of the line in the parametric form:

$\frac{x - x_{1}}{\cos θ} = \frac{y - y_{1}}{\sin θ} = \pm r \frac{x - 3}{4 / 5} = \frac{y - 2}{3 / 5} = \pm 5$

considering +5,

$x = 3 + \frac{4}{5} * 5 = 7 y = 2 + \frac{3}{5} * 5 = 5$ thus the coordinates are (7, 5)

for -5

$x = 3 - 4 = - 1 y = 2 - 3 = - 1$ thus coordinates are (-1,-1)

thus the coordinates of the required points are (-1, -1) and (7,5)

hope this helps you.

cheers!!

point (3,2) and whose slope is 3/4. find the coordinates of the points on the same line that are 5 units awa

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)