Problem

In triangle \(ABC\), a dilation centered at \(A\) maps segment \(BC\) to \(B'C'\). What conclusion about the image line or segment follows from the dilation?

Unworked dilation setup showing only the supplied center, source object, target if stated, and scale factor.

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What this problem is really about

The line-image theorem depends on whether the source side’s supporting line contains the dilation center. We’ll identify the center and source line, use the triangle’s noncollinearity to settle incidence, apply the invariant-or-parallel rule, and transfer the supporting-line result to the segment joining the corresponding image endpoints.

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B'C' is the same line as BC because a dilation keeps straight segments on the exact same line.

BC is parallel to B'C' because BC does not pass through the dilation center A.

B'C' must pass through A because the dilation is centered at A, so every image segment goes through the center.

BC and B'C' intersect at A because corresponding points in a dilation always make the original and image segments meet at the center.

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In triangle \(ABC\), a dilation centered at \(A\) maps segment \(BC\) to \(B'C'\). What conclusion about the image line or segment follows from the dilation?

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