Question

) Find the image of P(-5,2) after two transformations; first reflection over the y axis and thenrotated 90 counter clockwise about the origin.P'P”

Answer 1

$\begin{gathered} P^{\prime}(5,2) \\ P^{\prime\prime}\text{ (-2,5)} \end{gathered}$

Explanation

Step 1

The rule for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the y-value the same

$A(x,y)\rightarrow A^{\prime}(-x,y)$

then

$P(-5,2)\rightarrow P^{\prime}(-(-5).2)\rightarrow P^{\prime}(5,2)$

Step 2

then

rotated 90 counter clockwise about the origin.

When rotating a point 90 degrees counterclockwise about the origin our point P(x,y) becomes P'(-y,x). In other words, switch x and y and make y negative

$\begin{gathered} P(x,y)\rightarrow P(-y,x) \\ \end{gathered}$

then

$\begin{gathered} P^{\prime}(5,2)\rightarrow P^{\prime}^{\prime}\text{ (-2,5)} \\ P^{\prime\prime}\text{ (-2,5)} \end{gathered}$

I hope this helps you