Question

Calculate the ratio in which the line joining the points (-3,-1) and (5,7) is divided by the line x = 2. Also, find the coordinates of the points of intersection.

Answer 1

Answer:

given: points P (-3, -1) and Q (5, 7) divided by line x = 2 in some ratio.

to find the ratio, and coordinates of point of intersection

Step-by-step explanation:

let m and n be the ratio in which line joining the given points is getting divided by line x = 2

=> as line x = 2 divides the given line, coordinate of the point be say A (2, y)

=> Ax = (m x2 + n x1) / m+n

=> 2 = [m × 5 + n × (-3)] / m + n

=> 2 = (5m - 3n) / m + n

=> 2 ( m + n) = (5m - 3n)

=> 2m + 2n = 5m - 3n

=> 2m - 5m = - 3n - 2n

=> - 3m = - 5n

=> m/n = 5/3

therefore ratio is=>m : n = 5 : 3 [Answer 1]

now to find y of point A

Ay = (m y2 + n y1) / m + n

=> Ay = [5 × 7 + 3 × (-1)] / 5 + 3

=> Ay = (35 - 3) / 8

=> Ay = 32 / 8

=>Ay = 4

coordinates of A = (2, 4) [Answer 2]