Question

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dilate △abc by a scale factor of \\( \frac { 1 } { 2 } \\) with the center of dilation at point c.
\\( a ^ { \prime } c = 4 \\) units
\\( b ^ { \prime } c = 3 \\) units
move the points along the rays to plot
points \\( a ^ { \prime } \\) and \\( b ^ { \prime } \\).

Explanation:

Step1: Understand dilation concept

Dilation is a transformation that changes the size of a figure. When dilating with a scale factor \(k=\frac{1}{2}\) and center of dilation at \(C\), the distance from \(C\) to any point on the original figure (\(d\)) and the distance from \(C\) to the corresponding point on the dilated figure (\(d'\)) satisfy the relation \(d' = k\times d\).

Step2: Locate \(A'\)

Since \(A'C = 4\) units. Starting from \(C\), move 4 units along the ray \(CA\) (the direction from \(C\) to \(A\)) to plot \(A'\).

Step3: Locate \(B'\)

Since \(B'C=3\) units. Starting from \(C\), move 3 units along the ray \(CB\) (the direction from \(C\) to \(B\)) to plot \(B'\).

Answer:

Plot \(A'\) 4 units from \(C\) along \(CA\) and \(B'\) 3 units from \(C\) along \(CB\) on the given grid.