Question

date:
period: 2
congruence

1. determine a series of transformations that would map figure k onto figure l.

transformations:
is these two figure congruent or not congruent:

Explanation:

Step1: Rotate Figure K

Rotate Figure K \( 180^{\circ}\) about the origin. The rotation rule for a point \((x,y)\) rotated \(180^{\circ}\) about the origin is \((x,y)\to(-x, -y)\).

Step2: Translate the rotated figure

Translate the rotated figure. Count the vertical distance. The \(y -\)coordinate of a corresponding point on the rotated figure needs to be increased by \(7\) units. So, the translation rule is \((x,y)\to(x,y + 7)\).

Since a rotation (which is a rigid transformation, preserves shape and size) followed by a translation (also a rigid transformation, preserves shape and size) is used, the two figures are congruent.

Answer:

Transformations: Rotate Figure K \(180^{\circ}\) about the origin and then translate it \(7\) units up.
Congruence: The two figures are congruent.