Question

using the pencil, plot the reflection of point a across the x - axis.

Explanation:

Step1: Identify coordinates of A

Point A is on the y - axis. From the graph, we can see that the y - coordinate of A is - 7 (since it is 7 units below the origin) and the x - coordinate is 0. So, the coordinates of point A are \((0,-7)\).

Step2: Apply reflection rule over x - axis

The rule for reflecting a point \((x,y)\) across the x - axis is \((x,-y)\). For point A with coordinates \((0,-7)\), when we apply the reflection rule, the x - coordinate remains the same (\(x = 0\)) and the y - coordinate changes its sign. So, the y - coordinate of the reflected point will be \(-(-7)=7\).

Step3: Determine the reflected point

Using the reflection rule, the coordinates of the reflection of point A across the x - axis are \((0,7)\). To plot this point, we move 0 units along the x - axis (since \(x = 0\)) and 7 units up along the y - axis (since \(y = 7\)).

Answer:

The reflection of point A across the x - axis is at the point \((0,7)\) (and should be plotted at this location on the graph).