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:
= 5 + 6 + 4 = 14 in
= 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
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.
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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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
Step-by-step explanation:
