QuestionApril 20, 2026

Which set of transformations maps Delta ABC to Delta DEC and support Omar's thinking? a rotation of 180^circ clockwise about point C followed by a dilation with a center of point C and a scale factor of 2 a rotation of 180^circ clockwise about point C followed by a dilation with a center of point C and a scale factor of (1)/(2) a rotation of 180^circ counter-clockwise about point C followed by a dilation with a center of point C and a scale factor of 3 a rotation of 180^circ counter-clockwise about point C followed by a dilation with a center of point C and a scale factor of (1)/(3)

Which set of transformations maps Delta ABC to Delta DEC and support Omar's thinking? a rotation of 180^circ clockwise about point C followed by a dilation with a center of point C and a scale factor of 2 a rotation of 180^circ clockwise about point C followed by a dilation with a center of point C and a scale factor of (1)/(2) a rotation of 180^circ counter-clockwise about point C followed by a dilation with a center of point C and a scale factor of 3 a rotation of 180^circ counter-clockwise about point C followed by a dilation with a center of point C and a scale factor of (1)/(3)
Which set of transformations maps Delta ABC to Delta DEC and support Omar's thinking? a rotation of 180^circ clockwise about point C followed by a dilation with a center of point C and a scale factor of 2 a rotation of 180^circ clockwise about point C followed by a dilation with a center of point C and a scale factor of (1)/(2) a rotation of 180^circ counter-clockwise about point C followed by a dilation with a center of point C and a scale factor of 3 a rotation of 180^circ counter-clockwise about point C followed by a dilation with a center of point C and a scale factor of (1)/(3)

Solution
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Answer

a rotation of 180^{\circ} clockwise about point C followed by a dilation with a center of point C and a scale factor of 2 Explanation 1. Identify rotation equivalence A 180^\circ clockwise rotation is the same as a 180^\circ counter-clockwise rotation; only direction changes, but result is identical. 2. Determine scaling factor If \Delta ABC maps to \Delta DEC and Omar’s thinking involves enlargement, a scale factor > 1 is used; otherwise, reduction uses factor < 1. Scaling is about C, so C stays fixed. 3. Match correct transformation Enlargement after 180^\circ rotation about C fits scale factor 2, not \frac{1}{2}, 3, or \frac{1}{3}.

Explanation

1. Identify rotation equivalence <br /> A $180^\circ$ clockwise rotation is the same as a $180^\circ$ counter-clockwise rotation; only direction changes, but result is identical. <br /><br />2. Determine scaling factor <br /> If $\Delta ABC$ maps to $\Delta DEC$ and Omar’s thinking involves enlargement, a scale factor > 1 is used; otherwise, reduction uses factor < 1. Scaling is about C, so C stays fixed. <br /><br />3. Match correct transformation <br /> Enlargement after $180^\circ$ rotation about C fits scale factor $2$, not $\frac{1}{2}$, $3$, or $\frac{1}{3}$.
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