Question

Segment AB has endpoints with coordinates A: (-4, -7) and B: (8, -4). Determine the value of the x-coordinate of the interior point that separates Segment AB into lengths with a ratio of 8:5. Record answer to the nearest tenth.

Answer 1

≈ 3.4

Explanation:

Coordinates of the point that divide segment with endpoints A(
`x_(1)` ,
`y_(1)` ) and B(
`x_(2)` ,
`y_(2)` ) in a ratio a : b are

`(bx_(1) +ax_(2) )/(a+b)` ,
`(by_(1) +ay_(2) )/(a+b)` )

A(- 4, - 7)

B(8, - 4)

Ratio 8 : 5

x-coordinate is
`(5(-4)+8(8))/(8+5)` =
`(44)/(13)` ≈ 3.4