Question

lesson 3.1 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.
draw and label the final image of △abc after the given sequence of transformations.

1. reflect △abc over the x - axis and rotate 180 degrees around the origin.

transformation rule:

preimage abc	image abc	image abc
b(-3,4)
c(-2,5)

Explanation:

Step1: Reflection over x - axis rule

The rule for reflecting a point $(x,y)$ over the x - axis is $(x,-y)$.
For point $A(-1,2)$, after reflection over the x - axis, $A'(-1,-2)$.
For point $B(-3,4)$, after reflection over the x - axis, $B'(-3,-4)$.
For point $C(-2,5)$, after reflection over the x - axis, $C'(-2,-5)$.

Step2: Rotation 180 - degrees rule

The rule for rotating a point $(x,y)$ 180 degrees around the origin is $(-x,-y)$.
For $A'(-1,-2)$, after 180 - degree rotation, $A''(1,2)$.
For $B'(-3,-4)$, after 180 - degree rotation, $B''(3,4)$.
For $C'(-2,-5)$, after 180 - degree rotation, $C''(2,5)$.
The transformation rule for the combined transformation of reflection over the x - axis and 180 - degree rotation around the origin is $(x,y)\to(-x,y)$.

Answer:

Preimage ABC	Image A'B'C'	Image A''B''C''
$B(-3,4)$	$B'(-3,-4)$	$B''(3,4)$
$C(-2,5)$	$C'(-2,-5)$	$C''(2,5)$

Transformation rule: $(x,y)\to(-x,y)$