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
[tex]x-coordinate=\dfrac{mx_2+nx_1}{m+n}[/tex]
[tex]x-coordinate=\dfrac{1(-4)+7(-18)}{1+7}[/tex]
[tex]x-coordinate=\dfrac{-4-126}{8}[/tex]
[tex]x-coordinate=\dfrac{-130}{8}[/tex]
[tex]x-coordinate=-16.25[/tex]
Therefore, the required x-coordinate of point Z is -16.25.
