Question

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

Explanation:

Step1: Find coordinates of R, S, T

First, identify the coordinates of the vertices of \( \triangle RST \). From the graph:

• \( R \): Let's assume the grid. Looking at the points, \( R \) is at \( (-5, -10) \), \( S \) is at \( (-1, -10) \), \( T \) is at \( (-1, -4) \). Wait, actually, looking at the y-axis: the bottom is -10? Wait, no, the grid: each square is 1 unit. Let's recheck. The y-axis: the top is 10, bottom is -10. The x-axis is from -10 to 10. Let's find the coordinates:

• Point \( R \): Let's see, the x-coordinate: left of y-axis, so negative. Let's count the grid. From x=-5 (since between -6 and -4, maybe -5), y-coordinate: at y=-10? Wait, no, the purple triangle: R is at (-5, -10)? Wait, S is at (-1, -10), T is at (-1, -4). Wait, let's confirm:

Looking at the graph:

• \( R \): x = -5, y = -10 (since it's on the horizontal line at y=-10, x=-5)
• \( S \): x = -1, y = -10 (on y=-10, x=-1)
• \( T \): x = -1, y = -4 (on x=-1, y=-4)

Step2: Apply reflection over x-axis rule

The rule for reflection over the x-axis is: \( (x, y)
ightarrow (x, -y) \). So we apply this to each vertex.

• For \( R(-5, -10) \):

New coordinates: \( (-5, -(-10)) = (-5, 10) \)

• For \( S(-1, -10) \):

New coordinates: \( (-1, -(-10)) = (-1, 10) \)

• For \( T(-1, -4) \):

New coordinates: \( (-1, -(-4)) = (-1, 4) \)

Step3: Plot the new points

Now, plot the points \( R'(-5, 10) \), \( S'(-1, 10) \), and \( T'(-1, 4) \) on the coordinate plane and connect them to form the reflected triangle.

Answer:

The image of \( \triangle RST \) after reflection over the x - axis has vertices at \( R'(-5, 10) \), \( S'(-1, 10) \), and \( T'(-1, 4) \). (To graph, plot these points and connect them.)