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Back to Lines are taken to lines, and line segments to line segments of the same length — Problem 3 · Task Set 19

Exercises: Rigid Motions Preserve Lines and Lengths

Work through each section in order. For length calculations, use the distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Show your work where indicated.

Grade 8·20 problems·~30 min·Common Core Math - Grade 8·standard·8-g-a-1a
Work through problems with immediate feedback
A

Fluency Practice

Apply each transformation and verify the line- and length-preservation properties. Show your work.

1.

Segment PQPQ has endpoints P(2,1)P(2, 1) and Q(2,6)Q(2, 6). It is rotated 180°180\degree about the origin to give P′(−2,−1)P'(-2, -1) and Q′(−2,−6)Q'(-2, -6). What is the length of the image segment P′Q′P'Q'?