Task Sets: Lines are taken to lines, and line segments to line segments of the same length - Common Core Math - Grade 8

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.

$A coordinate grid showing segment AB and its translated image segment of the same length.$

Segment $AB$ has endpoints $A(1, 2)$ and $B(4, 6)$ , with length $5$ . Apply the translation $(x, y) \rightarrow (x + 3, y - 1)$ to get $A'$ and $B'$ . What is the length of the image segment $A'B'$ ?

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

$A coordinate grid showing segment CD and its reflection across the y-axis, both the same length.$

Segment $CD$ has endpoints $C(-3, 2)$ and $D(1, -1)$ . It is reflected across the y-axis to give $C'(3, 2)$ and $D'(-1, -1)$ . What is the length of the image segment $C'D'$ ?

Segment $EF$ has endpoints $E(0, 0)$ and $F(2, 3)$ . Its length is $\sqrt{13}$ . After a translation, the image endpoints are $E'(5, 1)$ and $F'(7, 4)$ . What is the length of $E'F'$ ? Give your answer as an exact value.

Exercises: Rigid Motions Preserve Lines and Lengths

Recall / Warm-Up

Fluency Practice