Question

graph the image of $\triangle rst$ after a reflection over the $x$-axis.

Explanation:

Step1: Identify coordinates of vertices

First, we find the coordinates of the vertices of $\triangle RST$. From the graph:

• $R$: Let's assume the grid. Looking at the points, $R$ is at $(-6, -10)$? Wait, no, wait. Wait, the y-axis at the bottom is -10? Wait, no, the grid lines. Wait, the point $R$: looking at the graph, $R$ is at $(-6, -10)$? Wait, no, let's check again. Wait, the point $S$ is at $(-2, -10)$, and $R$ is at $(-6, -10)$, and $T$ is at $(-2, -4)$. Wait, let's confirm:

• $R$: x = -6, y = -10 (since it's on the horizontal line at y=-10, x=-6)
• $S$: x = -2, y = -10 (on y=-10, x=-2)
• $T$: x = -2, y = -4 (on x=-2, y=-4)

Step2: Apply reflection over x-axis rule

The rule for reflecting a point $(x, y)$ over the x-axis is $(x, -y)$. So we apply this to each vertex:

• For $R(-6, -10)$: Reflect over x-axis: $(-6, -(-10)) = (-6, 10)$
• For $S(-2, -10)$: Reflect over x-axis: $(-2, -(-10)) = (-2, 10)$
• For $T(-2, -4)$: Reflect over x-axis: $(-2, -(-4)) = (-2, 4)$

Step3: Plot the reflected points

Now, we plot the reflected points:

• $R'(-6, 10)$
• $S'(-2, 10)$
• $T'(-2, 4)$

Then, connect these points to form the reflected triangle $\triangle R'S'T'$.

Answer:

To graph the image of $\triangle RST$ after reflection over the x - axis:

1. Find the coordinates of the original vertices: $R(-6, -10)$, $S(-2, -10)$, $T(-2, -4)$.
2. Apply the reflection rule over the x - axis: $(x, y)\to(x, -y)$.

• $R'(-6, 10)$
• $S'(-2, 10)$
• $T'(-2, 4)$

1. Plot these three points and connect them to form the reflected triangle.

(Note: The actual graphing would involve marking these points on the coordinate plane and drawing the triangle. The key is to use the reflection rule correctly to find the new coordinates.)