Question

Segment AB has endpoints on the coordinate grid where A is (- 18, 5) and B is (- 4, 5) Point Z is located exactly 1/8 of the distance from A to B. Determine the value of the x-coordinate of point

Answer 1

Given:

Endpoints of segment AB are A(- 18, 5) and B(- 4, 5).

Point Z is located exactly 1/8 of the distance from A to B.

To find:

The value of the x-coordinate of point Z.

Solution:

Point Z is located exactly 1/8 of the distance from A to B.

AZ:AB=1:8

AZ:ZB = AZ:(AB-AZ)= 1:(8-1) = 1:7

It means point Z divided segment AB in 1:7.

Using section formula, the x coordinate of point Z is

$x-coordinate=\dfrac{mx_2+nx_1}{m+n}$

$x-coordinate=\dfrac{1(-4)+7(-18)}{1+7}$

$x-coordinate=\dfrac{-4-126}{8}$

$x-coordinate=\dfrac{-130}{8}$

$x-coordinate=-16.25$

Therefore, the required x-coordinate of point Z is -16.25.