Question

reflect triangle efg across the line y = x. plot a point for each vertex.

Explanation:

Step1: Recall Reflection over \( y = x \)

To reflect a point \((a, b)\) across the line \( y = x \), we swap the \( x \)- and \( y \)-coordinates. So the reflection of \((a, b)\) is \((b, a)\).

Step2: Identify Coordinates of E, F, G

First, we need to find the coordinates of vertices E, F, G from the graph. Let's assume:

• Let \( E=(x_E, y_E) \), \( F=(x_F, y_F) \), \( G=(x_G, y_G) \). From the graph (estimating grid positions):
• Suppose \( E=(4, 5) \), \( F=(2, 4) \), \( G=(2, 1) \) (adjust based on actual grid, but the process is swapping \( x \) and \( y \)).

Step3: Reflect Each Point

• Reflect \( E=(4, 5) \): Swap \( x \) and \( y \), so \( E'=(5, 4) \).
• Reflect \( F=(2, 4) \): Swap \( x \) and \( y \), so \( F'=(4, 2) \).
• Reflect \( G=(2, 1) \): Swap \( x \) and \( y \), so \( G'=(1, 2) \).

Step4: Plot Reflected Points

Plot the points \( (5, 4) \), \( (4, 2) \), and \( (1, 2) \) on the coordinate plane.

Answer:

Reflect each vertex \((x, y)\) to \((y, x)\) and plot the new points. For example, if \( E=(4,5) \), \( F=(2,4) \), \( G=(2,1) \), their reflections are \( (5,4) \), \( (4,2) \), \( (1,2) \) respectively.