Question

name _______________
date _____________pd__
nsformations study guide
. be sure to ask questions if you need more help with a topic.
of orientation and congruence of transformations. 8.10ab
is. then, mark

1. translate the figure 8 units left and 2 units up.

then, mark the statements as true or false.
____ the pre-image is located in quadrant iii.
____ the pre-image and image are congruent
figures.

1. dilate the figure by a scale factor of 2.5.

then, mark the statements as true or false.

Explanation:

Step1: Identify pre-image coordinates

First, find the coordinates of the pre-image (figure STUV):

• $S=(1, -8)$
• $T=(1, -2)$
• $U=(5, -2)$
• $V=(5, -8)$

Step2: Verify pre-image quadrant

Quadrant III has $x<0, y<0$. The pre-image has $x>0, y<0$, so it is in Quadrant IV.
Statement 1: False

Step3: Apply translation rule

Translation: 8 left ($x-8$), 2 up ($y+2$). Calculate image coordinates:

• $S'=(1-8, -8+2)=(-7, -6)$
• $T'=(1-8, -2+2)=(-7, 0)$
• $U'=(5-8, -2+2)=(-3, 0)$
• $V'=(5-8, -8+2)=(-3, -6)$

Step4: Check congruence of translation

Translations are rigid transformations, so pre-image and image have identical shape/size (congruent).
Statement 2: True

Answer:

1. $\boldsymbol{\text{False}}$ (The pre-image is in Quadrant IV, not III)
2. $\boldsymbol{\text{True}}$ (Translations preserve congruence)

Translated image coordinates: $S'(-7, -6)$, $T'(-7, 0)$, $U'(-3, 0)$, $V'(-3, -6)$