Question

figure abcd is dilated from point q, the center of dilation. which figure is a dilation of figure abcd? figure efgh figure ijkl figure mnop

Explanation:

Step1: Recall the property of dilation

Dilation is a transformation that enlarges or reduces a figure by a scale factor with respect to a center point. The dilated figure and the original figure are similar (same shape).

Step2: Check figure \(EFGH\)

Figure \(EFGH\) is not centered at \(Q\). For dilation from point \(Q\), all corresponding points of the original and dilated figure should be collinear with \(Q\). Points of \(EFGH\) do not satisfy this collinearity property with \(Q\) as the center.

Step3: Check figure \(MNOP\)

Figure \(MNOP\) is not similar in shape to \(ABCD\). Dilation preserves the shape of the figure. \(MNOP\) has a different number of sides - \(ABCD\) is a rectangle (4 - sided) and \(MNOP\) is also 4 - sided, but if we consider the orientation and the proportion of side - lengths (by counting grid - units), the side - length ratios are not consistent for a dilation.

Step4: Check figure \(IJKL\)

For figure \(IJKL\), all corresponding points (e.g., if we consider a line from \(A\) through \(Q\) to \(I\), from \(B\) through \(Q\) to \(J\), from \(C\) through \(Q\) to \(K\), from \(D\) through \(Q\) to \(L\)) are collinear with the center of dilation \(Q\). Also, \(IJKL\) and \(ABCD\) are similar (both are rectangles)

Answer:

figure \(IJKL\)