Question

A right triangle with vertices P(-3,9) Q(-3,5) R(-7,5) is reflected on the y-axis then the image is rotated 180 degrees about the origin. What are new coordinates of the right triangle?

Answer 1

We could start by drawing the triangle we are given. However, it would be better to draw the triangle after the y-axis reflection. To calculate the y-axis reflection, we first think as follows

We see that the reflected point is at the same height as the original point. This means that the y coordinate should remain the same. So, the only thing that changed is the x coordinate. This suggests that, to calculate the reflection about the y-axis, we simply multiply by -1 the first coordinate. So, after the reflection we get the points

P'(-3*(-1),9)=(3,9)

Q'(-3*(-1),5)=(3,5)

R'(-7*(-1),5) =(7,5)

Now, if we plot this points we get

So, if we rotate this 180° we would get the following

So the new points after rotating 180°, would be

P''(-3,-9)

Q''(-3,-5)

R''(-7,-5)