Question

graph the image of rectangle stuv after a translation 12 units down.

Explanation:

Step1: Identify original coordinates

First, find the coordinates of the vertices of rectangle \( STUV \):

• \( S \): Let's assume from the grid, \( S = (-5, 4) \) (since it's 5 units left on x - axis and 4 units up on y - axis)
• \( T \): \( T = (-2, 4) \)
• \( U \): \( U = (-2, 6) \)
• \( V \): \( V = (-5, 6) \)

Step2: Apply translation (12 units down)

A translation 12 units down means we subtract 12 from the y - coordinate of each vertex. The translation rule for a point \( (x,y) \) is \( (x,y - 12) \).

• For \( S(-5,4) \): New coordinates \( S'=(-5,4 - 12)=(-5,-8) \)
• For \( T(-2,4) \): New coordinates \( T'=(-2,4 - 12)=(-2,-8) \)
• For \( U(-2,6) \): New coordinates \( U'=(-2,6 - 12)=(-2,-6) \)
• For \( V(-5,6) \): New coordinates \( V'=(-5,6 - 12)=(-5,-6) \)

Step3: Graph the new rectangle

Plot the points \( S'(-5,-8) \), \( T'(-2,-8) \), \( U'(-2,-6) \), \( V'(-5,-6) \) on the grid and connect them to form the translated rectangle.

Answer:

The translated rectangle \( S'T'U'V' \) has vertices at \( S'(-5,-8) \), \( T'(-2,-8) \), \( U'(-2,-6) \), \( V'(-5,-6) \). To graph it, plot these points and draw the sides connecting them.