Question

triangle m is the image of triangle m under a dilation.
what is the center of the dilation?
choose 1 answer:
a a
b b
c c
d d

Explanation:

To find the center of dilation, we use the property that the center of dilation lies on the line connecting each corresponding vertex of the original figure (triangle \( M \)) and its image (triangle \( M' \)). We can check the lines from the vertices of \( M \) and \( M' \) to each point (A, B, C, D).

For a dilation, the center is the point where the lines joining corresponding vertices intersect. Let's consider the vertices of \( M \) and \( M' \). When we draw lines from the vertices of \( M \) to \( M' \), we observe that these lines intersect at point \( B \).

• For point \( A \): The lines from vertices of \( M \) to \( M' \) do not pass through \( A \).
• For point \( C \): The lines from vertices of \( M \) to \( M' \) do not pass through \( C \).
• For point \( D \): The lines from vertices of \( M \) to \( M' \) do not pass through \( D \).
• For point \( B \): The lines connecting corresponding vertices of \( M \) and \( M' \) pass through \( B \), which satisfies the property of the center of dilation (it is the intersection point of lines joining corresponding vertices).

Answer:

B. \( B \)