Question

graphing a reflection in the coordinate plane
reflect △abc across the x - axis by answering the questions below and plotting the necessary points.

1. how many units away from the x - axis is point a?
2. the image of a will be 2 units away from the x - axis along the vertical line x = - 4. plot a.

Explanation:

Step1: Understand the reflection rule

When reflecting a point across the \(x\) - axis, the \(x\) - coordinate remains the same, and the \(y\) - coordinate changes its sign. The formula for reflecting a point \((x,y)\) across the \(x\) - axis is \((x,-y)\).

Step2: Determine the coordinates of point \(A\)

From the graph, point \(A\) is on the line \(x = - 4\). Since it is 2 units above the \(x\) - axis, the coordinates of point \(A\) are \((-4,2)\).

Step3: Find the coordinates of \(A'\)

Using the reflection rule \((x,y)\to(x,-y)\) with \(x=-4\) and \(y = 2\), for point \(A(-4,2)\), its reflection \(A'\) has coordinates \((-4,-2)\).

Answer:

Plot the point \(A'(-4,-2)\) on the coordinate plane.