Question

graph the image of △stu after a translation 3 units right and 10 units down.

Explanation:

Step1: Find coordinates of original points

First, identify the coordinates of \( \triangle STU \). From the graph:

• \( S \): \( (4, 2) \)
• \( T \): \( (4, 10) \)
• \( U \): \( (-5, 2) \)

Step2: Apply translation rules

A translation 3 units right means add 3 to the \( x \)-coordinate, and 10 units down means subtract 10 from the \( y \)-coordinate. The translation rule is \( (x, y) \to (x + 3, y - 10) \).

For \( S(4, 2) \):
\( x = 4 + 3 = 7 \), \( y = 2 - 10 = -8 \), so \( S' = (7, -8) \)

For \( T(4, 10) \):
\( x = 4 + 3 = 7 \), \( y = 10 - 10 = 0 \), so \( T' = (7, 0) \)

For \( U(-5, 2) \):
\( x = -5 + 3 = -2 \), \( y = 2 - 10 = -8 \), so \( U' = (-2, -8) \)

Step3: Graph the new points

Plot \( S'(7, -8) \), \( T'(7, 0) \), and \( U'(-2, -8) \) on the coordinate plane and connect them to form the translated triangle.

Answer:

The translated triangle \( \triangle S'T'U' \) has vertices at \( S'(7, -8) \), \( T'(7, 0) \), and \( U'(-2, -8) \). (Graphing these points on the given coordinate plane will show the image after translation.)