Question

1. draw the image of figure rstu after a translation 2 units left and 2 units down and a reflection across the y-axis. label the vertices.

Explanation:

Step1: Identify original vertices

From the grid: \( R(5,2) \), \( S(4,5) \), \( T(5,6) \), \( U(6,5) \)

Step2: Translate 2 left, 2 down

Rule: \( (x-2, y-2) \)
\( R'(5-2,2-2)=(3,0) \), \( S'(4-2,5-2)=(2,3) \), \( T'(5-2,6-2)=(3,4) \), \( U'(6-2,5-2)=(4,3) \)

Step3: Reflect over y-axis

Rule: \( (-x, y) \)
\( R''(-3,0) \), \( S''(-2,3) \), \( T''(-3,4) \), \( U''(-4,3) \)

Step4: Plot and label vertices

Connect \( R''(-3,0) \), \( S''(-2,3) \), \( T''(-3,4) \), \( U''(-4,3) \)

Answer:

The image vertices are \( R''(-3,0) \), \( S''(-2,3) \), \( T''(-3,4) \), \( U''(-4,3) \) (plot these on the grid to form the figure).