Question

Write the coordinates of the vertices after a reflection across the x-axis. P (-5, -7) -> P' (___,___)Q (-5, -2) -> Q' (___,___)R (-9, -10) -> R' (___,___)

Answer 1

The transformation rule for a reflection across the x-axis is:

`A(x,y)\longrightarrow A^(\prime)(x,-y)`

We will apply this rue to the three vertices.

Reflection across the x-axis of P:

`P(-5,-7)\longrightarrow P^(\prime)(-5,-(-7))`

In the image point, the x-coordinate remains the same, but we have to change the sign of the y-coordinate:

`P(-5,-7)\longrightarrow P^(\prime)(-5,7)`

Reflection across the x-axis of Q:

`Q(-5,-2)\longrightarrow Q^(\prime)(-5,-(-2))`

Simplifying the expression:

`Q(-5,-2)\longrightarrow Q^(\prime)(-5,2)`

Reflection across the x-axis of R:

`R(-9,-10)\longrightarrow R^(\prime)(-9,-(-10))`

simplifying the expression:

`R(-9,-10)\longrightarrow R^(\prime)(-9,10)`

Answer:

`\begin{gathered} P(-5,-7)\longrightarrow P^(\prime)(-5,7) \\ Q(-5,-2)\longrightarrow Q^(\prime)(-5,2) \\ R(-9,-10)\longrightarrow R^(\prime)(-9,10) \end{gathered}`