Question

draw the reflection of the triangle across the x-axis.

Explanation:

Step1: Identify original vertices

First, find the coordinates of the original triangle's vertices. Let's assume the original vertices (from the graph) are, for example, \( A(-8, -2) \), \( B(-5, -8) \), \( C(-3, -1) \) (we'll confirm the grid positions: each grid is 1 unit. So looking at the triangle, let's get accurate coordinates. Let's re - check:

Looking at the x - axis (horizontal) and y - axis (vertical). Let's list the three vertices:

Vertex 1: Let's say it's at \( (-8, -2) \) (x=-8, y=-2)

Vertex 2: At \( (-5, -8) \) (x=-5, y=-8)

Vertex 3: At \( (-3, -1) \) (x=-3, y=-1)

Step2: Apply reflection rule over x - axis

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

For vertex \( A(-8, -2) \):
Applying the rule, the reflected point \( A' \) is \( (-8, -(-2))=(-8, 2) \)

For vertex \( B(-5, -8) \):
The reflected point \( B' \) is \( (-5, -(-8)) = (-5, 8) \)

For vertex \( C(-3, -1) \):
The reflected point \( C' \) is \( (-3, -(-1))=(-3, 1) \)

Step3: Plot the reflected points

Plot the points \( A'(-8, 2) \), \( B'(-5, 8) \), and \( C'(-3, 1) \) on the coordinate plane and then connect them to form the reflected triangle.

(Note: Since this is a drawing problem, the key is to find the reflected coordinates of each vertex using the reflection rule over the x - axis (\( (x,y)\to(x, -y) \)) and then plot and connect them. If we were to describe the final drawing, the triangle would be above the x - axis, with vertices at the reflected coordinates we calculated.)

Answer:

To draw the reflection of the triangle across the x - axis:

1. Find the coordinates of the original triangle's vertices (e.g., let the original vertices be \( (-8, -2) \), \( (-5, -8) \), \( (-3, -1) \)).
2. Reflect each vertex using the rule \( (x,y)\to(x, -y) \) to get \( (-8, 2) \), \( (-5, 8) \), \( (-3, 1) \).
3. Plot these reflected points and connect them to form the reflected triangle.