Question

Find the coordinates of point L that lies along the directed line segment from N(14, 4) to M(2, 8) and partitions the segment in the ratio of 1:3.

Answer 1

The coordinates of L is (11, 5)

Explanation:

Points to remember

Let (x1, y1) and (x2, y2) be the points and P (x, y) be the points in which its divide the line segment in the ratio p : q,the coordinates of P is given by,

x = x1 + p/(w)(x2 - x1)

y = y1 + p/w(y2 - y1)

Where w = p + q

To find the coordinates of L(x, y)

Here, (x1, y1) = N(14, 4) and (x2, y2) = M(2, 8)

p = 1 and w = 1+3 = 4

x = x1 + p/(w)(x2 - x1)

= 14 + (1/4)(2 - 14)

= 14 + -3 = 11

y = y1 + p/w(y2 - y1)

= 4 + (1/4)(8 - 4)

= 4 + 1 = 5

Therefore the coordinates of L is (11, 5)