Question

the translation ((x - 10, y + 17)) is applied to a triangle. maryanne makes a conjecture about the perimeter of the image of the triangle, tests the conjecture, and finds that it is true. what could have been her conjecture?

• the perimeter of the image is 10 times the perimeter of the original triangle.
• the perimeter of the image is the same as the perimeter of the original triangle.
• the perimeter of the image is 10 units shorter than the perimeter of the original triangle.
• the perimeter of the image is 17 units longer than the perimeter of the original triangle.

Explanation:

A translation is a rigid transformation in geometry. Rigid transformations (like translation, rotation, reflection) do not change the shape or size of a figure. Since the perimeter depends on the lengths of the sides, and translation only moves the triangle without altering side lengths, the perimeter of the image (translated triangle) remains equal to the perimeter of the original triangle. The other options are incorrect because translation doesn't scale (so not 10 times), or change side lengths by adding/subtracting fixed units (10 or 17 units changes are wrong as translation is a positional change, not a length - altering one).

Answer:

B. The perimeter of the image is the same as the perimeter of the original triangle.