Question

write the coordinates of the vertices after a translation 5 units left and 7 units d

Explanation:

Step1: Find original coordinates

From the graph, the original coordinates are \( R(-1,-3) \), \( S(6,-3) \), \( T(9,5) \), \( U(1,5) \).

Step2: Apply translation rule

The translation rule for 5 units left (subtract 5 from \( x \)-coordinate) and 7 units down (subtract 7 from \( y \)-coordinate) is \((x,y)\to(x - 5,y - 7)\).

• For \( R(-1,-3) \): \( x=-1-5=-6 \), \( y=-3 - 7=-10 \), so \( R'(-6,-10) \).
• For \( S(6,-3) \): \( x=6-5 = 1 \), \( y=-3-7=-10 \), so \( S'(1,-10) \).
• For \( T(9,5) \): \( x=9-5=4 \), \( y=5 - 7=-2 \), so \( T'(4,-2) \).
• For \( U(1,5) \): \( x=1-5=-4 \), \( y=5 - 7=-2 \), so \( U'(-4,-2) \).

Answer:

\( R(-6,-10) \), \( S(1,-10) \), \( T(4,-2) \), \( U(-4,-2) \)