Question

which diagrams show a dilation centered at point o? select all that apply. a a o b b o c c d d save/exit

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. In a dilation centered at point \(O\), the lines connecting corresponding points of the original and dilated figure pass through \(O\).

Step2: Analyze each diagram

• Diagram \(A\): The lines connecting corresponding points of \(A\) and \(A'\) pass through \(O\). So it is a dilation centered at \(O\).
• Diagram \(B\): The lines connecting corresponding points of \(B'\) and \(B\) do not pass through \(O\). So it is not a dilation centered at \(O\).
• Diagram \(C\): The lines connecting corresponding points of \(C'\) and \(C\) do not pass through \(O\). So it is not a dilation centered at \(O\).
• Diagram \(D\): The lines connecting corresponding points of \(D\) and \(D'\) pass through \(O\). So it is a dilation centered at \(O\).

Answer:

The first and the fourth diagrams (the ones labeled \(A\) and \(D\)) show a dilation centered at point \(O\).