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, \( A(-7, -2) \), \( B(-3, -1) \), \( C(-5, -8) \) (we determine these by looking at the grid: x - coordinate (horizontal) and y - coordinate (vertical), with negative y for the original triangle below the x - axis).

Step2: Apply reflection rule over x - axis

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

• For vertex \( A(-7, -2) \), the reflected point \( A' \) will be \( (-7, -(-2))=(-7, 2) \)
• For vertex \( B(-3, -1) \), the reflected point \( B' \) will be \( (-3, -(-1))=(-3, 1) \)
• For vertex \( C(-5, -8) \), the reflected point \( C' \) will be \( (-5, -(-8))=(-5, 8) \)

Step3: Plot the reflected vertices

Plot the points \( A'(-7, 2) \), \( B'(-3, 1) \), and \( C'(-5, 8) \) on the coordinate grid and then connect them to form the reflected triangle.

(Note: Since this is a drawing task, the key is to use the reflection rule over the x - axis (\((x,y)\to(x, -y)\)) for each vertex of the original triangle and then draw the new triangle with the reflected vertices.)

Answer:

To draw the reflection of the triangle across the x - axis, follow these steps:

1. Find original vertices: Determine the coordinates of the three vertices of the given triangle (e.g., by reading their positions on the grid).
2. Reflect each vertex: Use the reflection rule over the x - axis: if a vertex has coordinates \((x,y)\), its reflection across the x - axis is \((x, -y)\).
3. Plot and connect: Plot the reflected vertices on the grid and draw line segments to connect them, forming the reflected triangle.

(Visually, the reflected triangle will be a mirror image of the original triangle with respect to the x - axis, with the y - coordinates of the vertices negated.)