Question

Polygon XYZW is dilated by a scale factor of 2 with point T as the center of dilation, resulting in the image X′Y′Z′W′. If point T lies on YZ¯¯¯¯¯, what can be said about Y'Z'¯¯¯¯¯¯¯ ?

Answer 1

The line segment Y'Z' will be twice the length of YZ after a dilation with a scale factor of 2, with T on YZ being the center of dilation.

Step-by-step explanation:

When polygon XYZW is dilated by a scale factor of 2 with point T as the center of dilation, and T lies on YZ, the line segment Y'Z' will be twice the length of YZ. This is because dilation scales all distances from the center of dilation by the scale factor, and since T is on YZ, that segment is directly scaled. All other points of the polygon not lying on YZ will also be moved away from their original positions while maintaining the original shape of the polygon but at a larger scale.