Question

determine the ratio in which the point 6,a divides the line segment joining the points a(9,-4), b(2,5). also find the value of A

Answer 1

Let the ratio in which the point P divides the line segment joining the points A(-4, 3) and B(2, 8) be 1:k.

y-coordinate of point P =

[(8 + 3k) / (1 + k)] = 6

By cross multiplication,

8 + 3k = 6 + 6k

3k = 2

k = 2/3

So, the ratio in which the point divides AB = 1 : 2/3 = 3 : 2

x-coordinate of P

= [(6 - 8) / (3 + 2)] = -2/5.

Hence, the value of m is -2/5.