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

Answer:

 ≈ 3.4

Step-by-step 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

$\frac{bx_{1} +ax_{2} }{a+b}$ , $\frac{by_{1} +ay_{2} }{a+b}$ )

A(- 4, - 7)

B(8, - 4)

Ratio 8 : 5

x-coordinate is $\frac{5(-4)+8(8)}{8+5}$ = $\frac{44}{13}$ ≈ 3.4