Question

which figure is a dilation of figure e? figure f figure g figure h

Explanation:

Step1: Recall the definition of dilation

Dilation is a transformation that enlarges or reduces a figure by a scale factor relative to a center point. The dilated figure is similar to the original figure (same shape, different size).

Step2: Check the similarity of shapes

• Figure \(E\) is a rectangle - like shape (a right - angled figure).
• Figure \(F\):
• If we consider the center of dilation \(D\), the sides of figure \(F\) are in proportion to the sides of figure \(E\). Let's assume the horizontal and vertical side lengths of figure \(E\). Suppose the horizontal side of \(E\) has length \(l_E\) and the vertical side has length \(v_E\). For figure \(F\), if we count the grid - units (assuming each grid - square has side - length \(1\)), and use the property of similar figures (for dilation, \(\frac{l_F}{l_E}=\frac{v_F}{v_E} =\text{scale factor}\)).
• For example, if the horizontal side of \(E\) is \(2\) units and the horizontal side of \(F\) is \(4\) units, and the vertical side of \(E\) is \(1\) unit and the vertical side of \(F\) is \(2\) units. The scale factor \(k = 2\) (since \(\frac{4}{2}=\frac{2}{1}=2\)).
• Figure \(G\):
• The shape of \(G\) is not similar to \(E\) in terms of the right - angle side - length ratios. If we check the side - length ratios (using grid - units), \(\frac{\text{horizontal side of }G}{\text{horizontal side of }E}

eq\frac{\text{vertical side of }G}{\text{vertical side of }E}\).

• Figure \(H\):
• The shape of \(H\) is not similar to \(E\) in terms of the right - angle side - length ratios. If we check the side - length ratios (using grid - units), \(\frac{\text{horizontal side of }H}{\text{horizontal side of }E}

eq\frac{\text{vertical side of }H}{\text{vertical side of }E}\).

Answer:

figure \(F\)