Question

Given directed line segment with endpoints A(-3, 1) and B(5, 13), what is the coordinate that partitions the line segment into a ratio of 1:3?

A(4, –1)

B(–1, 4)

C(–⅓, 5)

D(5, –⅓)

Answer 1

B(–1, 4)

Explanation:

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

Since it is on the directed line segment AB in the ratio 1:3, it means that:

`P - A = (1)/(1+3)(B-A)`

So

`P - A = (1)/(4)(B-A)`

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

x-coordinate:

x-coordinate of A: -3

x-coordinate of B: 5

x-coordinate of P: x

So

`P - A = (1)/(4)(B-A)`

`x - (-3) = (1)/(4)(5 - (-3))`

`x + 3 = (1)/(4) * 8`

`x + 3 = 2`

`x = -1`

y-coordinate:

y-coordinate of A: 1

y-coordinate of B: 13

y-coordinate of P: y

So

`P - A = (1)/(4)(B-A)`

`y - 1 = (1)/(4)(13 - 1)`

`y - 1 = (1)/(4) * 12`

`y - 1 = 3`

`y = 4`

So the correct answer is given by option B.