Back to Lines are taken to lines, and line segments to line segments of the same length — Problem 1 · 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

Fluency Practice

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

$A coordinate grid showing five original points on a rising line with a dashed arrow indicating the translation direction; the image points are not shown.$

The line through the points $(-2, -1), (-1, 0), (0, 1), (1, 2), (2, 3)$ is translated by the rule $(x, y) \rightarrow (x + 4, y - 2)$ . After translating all five points, what is true about the images?

The five image points lie on a straight line.

The five image points form a curve.

The image points are scattered and not collinear.

Only three of the five image points lie on a line.