Question

1. reflect xyz about the y - axis and then translate xyz 4 units up. find the indicated coordinates. z ( , ) y ( , ) x ( , )

Explanation:

Step1: Find coordinates of \( X,Y,Z \)

Assume \( X(-1,2) \), \( Y(-6,8) \), \( Z(-9,4) \)

Step2: Reflect over \( y - axis \)

The rule for reflection over \( y - axis \) is \( (x,y)\to(-x,y) \).
So \( X'=(1,2) \), \( Y'=(6,8) \), \( Z'=(9,4) \)

Step3: Translate 4 units up

The rule for translation 4 units up is \( (x,y)\to(x,y + 4) \)
For \( X'' \): \( x = 1,y=2 + 4=6 \), so \( X''(1,6) \)
For \( Y'' \): \( x = 6,y=8 + 4=12 \), so \( Y''(6,12) \)
For \( Z'' \): \( x = 9,y=4+4 = 8 \), so \( Z''(9,8) \)

Answer:

\( X''(1,6) \), \( Y''(6,12) \), \( Z''(9,8) \)