Which statement proves that the dilation of △ XYZ does not pass through the center of dilation? (1 point) Responses XY and X′Y' both have an undefined slope with a center of dilation at (0,0) . This proves that the lines are parallel and that the dilation does not pass through the center of dilation. XY and X′Y' both have an undefined slope with a center of dilation at (0,0) . This proves that the lines are parallel and that the dilation does not pass through the center of dilation. Responses XY has a length of 3 and X′Y′ has a length of 1, which proves that ΔXYZ is a dilation of ΔX′Y′Z′ by a scale factor of 3. Responses XY has a length of 3 and X′Y′ has a length of 1, which proves that ΔXYZ is a dilation of ΔX′Y′Z′ by a scale factor of 3. XY has a length of 3 and X′Y′ has a length of 1, which proves that ΔX′Y′Z′ is a dilation of ΔXYZ by a scale factor of 13 . XY has a length of 3 and X′Y′ has a length of 1, which proves that ΔX′Y′Z′ is a dilation of ΔXYZ by a scale factor of 13 . X′(−3⋅1/3,−3⋅1/3)=X′(−1,−1) , Y′(−3⋅1/3,−6⋅1/3)=Y′(−1,−2) , Z′(−6⋅1/3,−3⋅1/3)=Z′(−2,−1) .

Answer 1

The statement that proves that the dilation of △XYZ does not pass through the center of dilation is:

"XY and X′Y′ both have an undefined slope with a center of dilation at (0,0). This proves that the lines are parallel and that the dilation does not pass through the center of dilation."

This statement shows that the original line segment and its dilated image do not intersect at the center of dilation, thus indicating that the dilation is not centered at that point.