Problem

Do these figures match after this rigid-motion sequence: translate by \(<2,2>\), then reflect over the \(x\text{-}\text{axis}\)? Compare preimage vertices \((1,1)\), \((3,1)\), and \((1,4)\) with image vertices \((3,-3)\), \((5,-3)\), and \((3,-5)\).

Answer choices

Choose your path.

Preview only

Yes, because reflecting the preimage first gives (1,-1), (3,-1), and (1,-4), and then translating by <2,2> makes the figures line up with the image.

No, because translating the preimage gives (3,3), (5,3), and (3,6), and reflecting over the x-axis gives (3,-3), (5,-3), and (3,-6), so the last point does not match (3,-5).

Yes, because after the translation and reflection, the points (3,-3) and (5,-3) match the image, so the figures must match.

Yes, because after translating to (3,3), (5,3), and (3,6), reflecting over the x-axis changes both coordinates to negatives, so the image matches.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Do these figures match after this rigid-motion sequence: translate by \(<2,2>\), then reflect over the \(x\text{-}\text{axis}\)? Compare preimage vertices \((1,1)\), \((3,1)\), and \((1,4)\) with image vertices \((3,-3)\), \((5,-3)\), and \((3,-5)\).

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.