Question

In traingle XYZ, XY = 5 in, YZ= 6 in, and XZ = 4 in. This triangle is reflected across the x axis to result triangle XYZ. Which is true ?

Answer 1

Note: As you have not added the answer choices, but after a little research I was able to find out that this question had contained a choice that mentioned the perimeter of resulting triangle △X'Y'Z' = 15 in. So, I am explaining the concept of reflection across x-axis of a triangle, that would anyways clear your concept.

Answer:

• The perimeter of △XYZ = XY + YZ + XZ

                                                = 5 + 6 + 4 = 14 in

• The perimeter of △X'Y'Z' = X'Y' + Y'Z' + X'Z'

                                                   = 5 + 6 + 4 = 14 in

Therefore, the perimeter of △X'Y'Z would be equal to the perimeter of △X'Y'Z.

Step-by-step explanation:

As the given triangle △XYZ

• XY = 5 in

• YZ= 6 in

• XZ = 4 in

As we know that reflection is a rigid transformation that does not change the length. i.e. the lengths remain preserved in rigid transformation.

So, as this triangle △XYZ is reflected across the x-axis to result in △X'Y'Z' . It means the corresponding sides of △X'Y'Z' will have the same lengths.

• XY = 5 in ⇒ X'Y' = 5 in
• YZ = 6 in ⇒ Y'Z' = 6 in
• XZ = 4 in ⇒ X'Z' = 4 in

As the perimeter of any triangle is the sum of the lengths of the sides of a triangle.

So,

The perimeter of △XYZ = XY + YZ + XZ

                                        = 5 + 6 + 4 = 14 in

Then

The perimeter of △X'Y'Z' = X'Y' + Y'Z' + X'Z'

                                          = 5 + 6 + 4 = 14 in

Therefore, the perimeter of △X'Y'Z would be equal to the perimeter of △X'Y'Z.

i.e.

The perimeter of △XYZ = The perimeter of △X'Y'Z'

Keywords: rigid transformation, reflection across the x-axis, perimeter

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