Question

Triangle XYZ with vertices X ( 5 , 7 ) , Y ( 8 , 3 ) , and Z ( 2 , 3 ) is reflected over the y-axis and translated up 4 units to form triangle X ` Y ` Z ` . What is the length of segment Y ` Z ` ?

Answer 1

After the reflection and the translation of XYZ, the length of segment Y'Z'  is 6 units

How to determine the length of segment Y'Z' ?

The transformation is given as:

• Reflection across the y-axis
• Translation 4 units up

Both transformations are rigid transformations.

This means that the lengths YZ and Y'Z' would remain the same

The coordinates are given as:

Y = (8,3)

Z = (2,3)

Both points are on the same y coordinate.

So, the length YZ is

YZ = 8 - 2

Evaluate

YZ = 6

Hence, the length of segment Y'Z'  is 6 units

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