Question

identify the reflection of the figure with vertices P (2, -12), Q (-3, 13), and R (-5, - 15) across the x-axis.

Answer 1

Step-by-step explanation:

We are given the following coordinates for a figure on the coordinate plane;

`\begin{gathered} P(2,-12) \\ Q(-3,13) \\ R(-5,-15) \end{gathered}`

To reflect any figure or any set of coordinates across the x-axis, we shall apply the rule;

`(x,y)\rightarrow(x,-y)`

Note that the x-coordinate remains the same whereas, the y-coordinate changes its sign.

Imagine folding a graph page in two equal halves along the horizontal axis. You'll observe the y-coordinates will switch sides from top to bottom (positive to negative) or bottom to top (negative to positive). The x-coordinate remains the same since moving the folded page does not affect values along the horizontal line.

Therefore, for the vertices given, the reflection across the x-axis would be;

`P(2,-12)\rightarrow P^(\prime)(2,12)`
`Q(-3,13)\rightarrow Q^(\prime)(-3,-13)`
`R(-5,-15)\rightarrow R^(\prime)(-5,15)`

ANSWER:

The coordinates of the reflection across the x-axis therefore will be;

`\begin{gathered} P^(\prime)(2,12) \\ Q^(\prime)(-3,-13) \\ R^(\prime)(-5,15) \end{gathered}`