Answer to Question #138283 in Geometry for David

Question

Y is the midpoint of XZ and XZ = 20, what are the lengths of XY and YZ?

Answer 1

Since $Y$ is the midpoint of $XZ$,

and $XZ = 20$

$\therefore$ $XY + YZ = XZ$

$XY + YZ = 20$

but, the distance from X to Y is equal to the distance form Y to Z

so, $XY=YZ$

$\therefore XY + XY = 20$

$2XY = 20$

$XY = 10$

Since $XY = YZ$,

$XY=YZ=10$

$\therefore XY = 10 \quad; \quad YZ = 10$