Question

lesson 1.3 checkpoint
once you have completed the above problems and checked your solutions, complete the lesson checkpoint below.
complete the lesson reflection above by circling your current understanding of the learning goal.

1. draw the image of the figure under the given transformation. then describe the transformation as a rigid motion or not a rigid motion. justify your answer.

(x,y)→(0.5x,y - 4)
d (-4, 3)
e (2, 3)
f (4, 1)

Explanation:

Step1: Apply transformation to point D

For point D(-4, 3), substitute \(x=-4\) and \(y = 3\) into \((x,y)\to(0.5x,y - 4)\).
\(x'=0.5\times(-4)=-2\), \(y'=3 - 4=-1\). So D' is (-2,-1).

Step2: Apply transformation to point E

For point E(2, 3), substitute \(x = 2\) and \(y=3\) into \((x,y)\to(0.5x,y - 4)\).
\(x'=0.5\times2 = 1\), \(y'=3-4=-1\). So E' is (1,-1).

Step3: Apply transformation to point F

For point F(4, 1), substitute \(x = 4\) and \(y = 1\) into \((x,y)\to(0.5x,y - 4)\).
\(x'=0.5\times4=2\), \(y'=1 - 4=-3\). So F' is (2,-3).

Step4: Determine if it's a rigid - motion

A rigid motion preserves distance and angle. The transformation \((x,y)\to(0.5x,y - 4)\) is a non - rigid motion because the \(x\) - coordinate is multiplied by 0.5, which changes the distances between points. For example, the distance between two points in the original figure and the transformed figure will not be the same.

Answer:

The image of D(-4, 3) is D'(-2,-1), the image of E(2, 3) is E'(1,-1), and the image of F(4, 1) is F'(2,-3). The transformation \((x,y)\to(0.5x,y - 4)\) is not a rigid motion because the \(x\) - coordinate is scaled by a factor of 0.5, which changes the distances between points.