Question

graph the image of δstu after a reflection over the x-axis.

Explanation:

Step1: Find coordinates of S, T, U

First, we determine the coordinates of the vertices of $\triangle STU$. From the graph:

• Point \( S \): Let's look at the grid. The x - coordinate of \( S \) is - 4, and the y - coordinate is - 3. So \( S=(-4,-3) \)
• Point \( T \): The x - coordinate of \( T \) is 6, and the y - coordinate is - 3. So \( T=(6,-3) \)
• Point \( U \): The x - coordinate of \( U \) is - 4, and the y - coordinate is - 7. So \( U=(-4,-7) \)

Step2: Apply reflection over x - axis rule

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

• For point \( S(-4,-3) \):

Applying the rule, the new x - coordinate is - 4 (same as original x - coordinate), and the new y - coordinate is \(-(-3) = 3\). So the image of \( S \), let's call it \( S' \), is \( S'=(-4,3) \)

• For point \( T(6,-3) \):

Applying the rule, the new x - coordinate is 6, and the new y - coordinate is \(-(-3)=3\). So the image of \( T \), \( T'=(6,3) \)

• For point \( U(-4,-7) \):

Applying the rule, the new x - coordinate is - 4, and the new y - coordinate is \(-(-7) = 7\). So the image of \( U \), \( U'=(-4,7) \)

Step3: Plot the new points

Now, we plot the points \( S'(-4,3) \), \( T'(6,3) \), and \( U'(-4,7) \) on the coordinate plane and connect them to form the reflected triangle \(\triangle S'T'U'\).

(Note: Since the problem asks to graph the image, the final answer is the graph with the reflected points. But in terms of the coordinates of the reflected triangle, the vertices are \( S'(-4,3) \), \( T'(6,3) \), \( U'(-4,7) \))

Answer:

The image of \(\triangle STU\) after reflection over the x - axis has vertices \( S'(-4,3) \), \( T'(6,3) \), and \( U'(-4,7) \). To graph it, plot these points and connect them.