Question

Given point A (-9, -9) and B (5, -2) find the coordinates of point P on the directed line segment AB in the ratio 3:4.

Answer 1

Answer:

We have point P(-3,-6).

Step-by-step explanation:

We want to find a point P(x,y).

Since it is on the directed line segment AB in the ratio 3:4, it means that:

$P - A = \frac{3}{3+4}(B - A)$

So

$P - A = \frac{3}{7}(B-A)$

We apply this to both the x-coordinate and y-coordinate of P.

x-coordinate:

x-coordinate of A: -9

x-coordinate of B: 5

x-coordinate of P: x

So

$P - A = \frac{3}{7}(B-A)$

$x - (-9) = \frac{3}{7}(5-(-9))$

$x + 9 = \frac{3}{7} \times 14$

$x + 9 = 6$

$x = -3$

y-coordinate:

y-coordinate of A: -9

y-coordinate of B: -2

y-coordinate of P: y

So

$P - A = \frac{3}{7}(B-A)$

$y - (-9) = \frac{3}{7}(-2-(-9))$

$y + 9 = \frac{3}{7} \times 7$

$y + 9 = 3$

$y = -6$

We have point P(-3,-6).