Question

graph the image of △tuv after a reflection over the y-axis.

Explanation:

Step1: Find coordinates of vertices

First, identify the coordinates of \( T \), \( U \), and \( V \) from the graph.

• \( T \): \( (-4, 3) \) (since it's 4 units left of y - axis and 3 units up)
• \( U \): \( (-4, 6) \) (4 units left, 6 units up)
• \( V \): \( (-10, 2) \) (10 units left, 2 units up)

Step2: Apply reflection over y - axis rule

The rule for reflecting a point \((x,y)\) over the \( y \) - axis is \((x,y)\to(-x,y)\).

• For \( T(-4,3) \): Apply the rule, \( x=-4\), so \(-x = 4\). New coordinates \( T'(4,3) \)
• For \( U(-4,6) \): \( x = - 4\), \(-x=4\). New coordinates \( U'(4,6) \)
• For \( V(-10,2) \): \( x=-10\), \(-x = 10\). New coordinates \( V'(10,2) \)

Step3: Plot the new points

Plot the points \( T'(4,3) \), \( U'(4,6) \), and \( V'(10,2) \) on the coordinate plane and connect them to form the reflected triangle \( \triangle T'U'V' \).

Answer:

The image of \( \triangle TUV \) after reflection over the \( y \) - axis has vertices at \( T'(4,3) \), \( U'(4,6) \), and \( V'(10,2) \). (To graph, plot these points and connect them.)