Question

Triangle XYZ with vertices 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'?

A) The length remains the same.
B) The length is 4 units.
C) The length is twice the length of segment YZ.
D) The length is 8 units.

Answer 1

When a triangle is reflected over the y-axis and translated up, the length of segment Y'Z' remains the same as the length of segment YZ in the original triangle XYZ.

Step-by-step explanation:

When a triangle is reflected over the y-axis, the x-coordinates of its vertices change sign while the y-coordinates remain the same. So, triangle XYZ becomes triangle X'Y'Z', where the x-coordinates of X', Y', and Z' are -x, -y, and -z respectively.

Next, when a triangle is translated up by 4 units, all the y-coordinates of its vertices increase by 4. So, the new y-coordinates of X', Y', and Z' are y+4, z+4, and x+4 respectively.

Therefore, the length of segment Y'Z' is equal to the length of segment YZ in the original triangle XYZ. So the correct answer is A) The length remains the same.