Question

On a number line, the coordinates of X, Y, Z, and W are -7, -3, 1, and 5, respectively. Find the lengths of the two segments below. Then tell whether they are congruentXY and ZWThe length of XY isThe length of ZW is(Type an integer or a decimal.)(Type an integer or a decimal.)

Answer 1

The Solution:

Given:

$\begin{gathered} X=-7 \\ Y=-3 \\ Z=1 \\ W=5 \end{gathered}$

Required:

Determine whether segment XY is congruent to segment ZW.

Step 1:

Find the length of segment XY.

$XY=-3-(-7)=-3+7=4$

Step 2:

Find the length of segment ZW.

$ZW=5-1=4$

Since:

$\begin{gathered} XY=ZW=4 \\ It\text{ follows that XTY and ZW are congruent.} \end{gathered}$

Answer:

XY = 4

ZW = 4

They are congruent.