Question

write the coordinates of the vertices after a translation 5 units up.
r((□,□))
s((□,□))
t((□,□))

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of \( R \), \( S \), and \( T \) from the graph.

• \( R \) is at \( (0, -3) \) (since it's on the y - axis, x = 0, and y=-3).
• \( S \) is at \( (0, 5) \) (on the y - axis, x = 0, y = 5).
• \( T \) is at \( (9, -5) \) (x = 9, y=-5).

Step2: Apply translation (5 units up)

A translation of 5 units up means we add 5 to the y - coordinate of each point (the x - coordinate remains the same). The rule for a translation 5 units up is \( (x,y)\to(x,y + 5) \).

For \( R \):

Original coordinates of \( R=(0,-3) \). After translation, \( x \) remains 0, and \( y=-3 + 5=2 \). So \( R'=(0,2) \).

For \( S \):

Original coordinates of \( S=(0,5) \). After translation, \( x = 0 \), and \( y=5 + 5 = 10 \). So \( S'=(0,10) \).

For \( T \):

Original coordinates of \( T=(9,-5) \). After translation, \( x = 9 \), and \( y=-5+5 = 0 \). So \( T'=(9,0) \).

Answer:

For \( R' \): \( (0, 2) \)
For \( S' \): \( (0, 10) \)
For \( T' \): \( (9, 0) \)

(If we only consider \( R' \) as per the boxed part in the question, the answer for \( R' \) is \( (0,2) \))