Question

Line segment AB is given by the coordinates A (-4, 16) and B (-4, 32). Find the two sets of coordinates that could partition this segment in the ratio 3:1 or 1:3.

Answer 1

The required sets of coordinates are (-4,28) and (-4,20).

Explanation:

Given information: A (-4, 16) and B (-4, 32).

Section formula:

If end point of a line segment are
`(x_1,y_1)` and
`(x_2,y_2)` and a point divides that line segment in m:n, then the coordinates of that point are

`((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n))`

If a point divides AB in 3:1, then coordinates of that point are

`(((3)(-4)+(1)(-4))/(3+1),((3)(32)+(1)(16))/(3+1))`

`((-12-4)/(4),(96+16)/(4))`

`((-16)/(4),(112)/(4))`

`(-4,28)`

If a point divides AB in 1:3, then coordinates of that point are

`(((1)(-4)+(3)(-4))/(1+3),((1)(32)+(3)(16))/(1+3))`

`((-4-12)/(4),(32+48)/(4))`

`((-16)/(4),(80)/(4))`

`(-4,20)`

Therefore the required sets of coordinates are (-4,28) and (-4,20).