Question

graph the image of δstu after a translation 2 units right and 6 units down.

Explanation:

Step1: Identify original coordinates

First, find the coordinates of points \( S \), \( T \), and \( U \) from the graph.

• \( S(-8, -1) \) (since it's 8 units left on x - axis and 1 unit down on y - axis)
• \( T(-8, 0) \) (8 units left on x - axis and on y = 0)
• \( U(0, 1) \) (on y - axis, 1 unit up)

Step2: Apply translation rules

A translation of \( h \) units right and \( k \) units down is given by the rule \((x,y)\to(x + h,y - k)\). Here, \( h = 2 \) (2 units right) and \( k=6 \) (6 units down).

For point \( S(-8,-1) \):
New \( x \)-coordinate: \(-8 + 2=-6\)
New \( y \)-coordinate: \(-1-6 = -7\)
So, \( S'(-6,-7) \)

For point \( T(-8,0) \):
New \( x \)-coordinate: \(-8 + 2=-6\)
New \( y \)-coordinate: \(0 - 6=-6\)
So, \( T'(-6,-6) \)

For point \( U(0,1) \):
New \( x \)-coordinate: \(0+2 = 2\)
New \( y \)-coordinate: \(1-6=-5\)
So, \( U'(2,-5) \)

Step3: Graph the new points

Plot the points \( S'(-6,-7) \), \( T'(-6,-6) \), and \( U'(2,-5) \) on the coordinate plane and connect them to form the image of \( \triangle STU \) after translation.

Answer:

The image of \( \triangle STU \) has vertices at \( S'(-6,-7) \), \( T'(-6,-6) \), and \( U'(2,-5) \). (To graph, plot these points and draw the triangle.)