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Dilations and Similar Figures — Mixed

A dilation multiplies every coordinate by the scale factor. Show your work.

ExampleA(1, 1), B(3, 1), C(1, 3) was dilated about the origin to A′(2, 2), B′(6, 2), C′(2, 6). → Scale factor 2. Every side doubles and every angle is unchanged, so the figures are similar.
  1. 1.xy−7−7−6−6−5−5−4−4−3−3−2−2−1−111223344556677ABCA′B′C′
    Triangle ABC was dilated about the origin to give A′B′C′. What is the scale factor, and why are the two figures similar?
    Scale factor
    Why similar?
  2. 2.xy−7−7−6−6−5−5−4−4−3−3−2−2−1−111223344556677ABCDA′B′C′D′
    Triangle ABCD was dilated about the origin to give A′B′C′D′. Write the coordinates of A′, B′, C′, D′ and give the scale factor.
    A′   B′   C′   D′    Scale factor
  3. 3.xy−10−10−8−8−6−6−4−4−2−2224466881010ABCA′B′C′
    Triangle ABC was dilated about the origin to give A′B′C′. Write the coordinates of A′, B′, C′ and give the scale factor.
    A′   B′   C′    Scale factor
  4. 4.xy−7−7−6−6−5−5−4−4−3−3−2−2−1−111223344556677ABCA′B′C′
    Triangle ABC was dilated about the origin to give A′B′C′. Write the coordinates of A′, B′, C′ and give the scale factor.
    A′   B′   C′    Scale factor
  5. 5.xy−7−7−6−6−5−5−4−4−3−3−2−2−1−111223344556677ABCDA′B′C′D′
    Triangle ABCD was dilated about the origin to give A′B′C′D′. Write the coordinates of A′, B′, C′, D′ and give the scale factor.
    A′   B′   C′   D′    Scale factor