Question

What are the coordinates of the point that divides the directed segment from (-1,4) to (-9,0) in the ratio 1:3?

a) (-7,2)
b) (-5,1)
c) (-3,0)
d) (-11,3)

Answer 1

The coordinates of the point that divides the directed segment from (-1,4) to (-9,0) in the ratio 1:3 are (-7,2).

Step-by-step explanation:

To find the coordinates of the point that divides the directed segment from (-1,4) to (-9,0) in the ratio 1:3, we can use the section formula. The section formula states that if a line segment AB is divided by a point P(x, y) in the ratio m:n, then the coordinates of P are given by:

x = (mx2 + nx1) / (m + n)

y = (my2 + ny1) / (m + n)

Plugging in the given values, we get:

x = (1(-9) + 3(-1)) / (1 + 3) = -7

y = (1(0) + 3(4)) / (1 + 3) = 2

Therefore, the point that divides the directed segment in the ratio 1:3 is (-7, 2).