Question

graph the image of (\triangle uvw) after a reflection over the line (y = -x).

Explanation:

Step1: Find coordinates of points

From the graph, we have \( M(-9,5) \), \( U(-4,7) \), \( V(-4,-1) \).

Step2: Apply reflection rule

The rule for reflection over the line \( y = -x \) is \( (x,y)\to(-y,-x) \).

• For point \( M(-9,5) \):

Substitute \( x=-9 \), \( y = 5 \) into the rule \( (x,y)\to(-y,-x) \).
We get \( M'(-5,9) \).

• For point \( U(-4,7) \):

Substitute \( x=-4 \), \( y = 7 \) into the rule \( (x,y)\to(-y,-x) \).
We get \( U'(-7,4) \).

• For point \( V(-4,-1) \):

Substitute \( x=-4 \), \( y=-1 \) into the rule \( (x,y)\to(-y,-x) \).
We get \( V'(1,4) \).

Step3: Plot the reflected points

Plot \( M'(-5,9) \), \( U'(-7,4) \), \( V'(1,4) \) on the coordinate plane and connect them to form the reflected triangle.

Answer:

The coordinates of the reflected triangle are \( M'(-5,9) \), \( U'(-7,4) \), \( V'(1,4) \). Plot these points and connect them.