Question

PQ is rotated 180 degrees clockwise about P. What are the coordinates of P' and Q'?

Answer 1

The co ordinates of P' is (-7,-2) and Q' is (-16, -8)

Explanation

PQ is rotated 180 degrees clockwise about P. It means P and P' are the same points.

According to the graph, the coordinates of P is (-7, -2) and  Q is (2, 4)

When PQ is rotated 180 degrees clockwise about P, then P or P' will be the mid-point of Q and Q'

Suppose, the co ordinate of Q' is (x, y)

Now according to the mid-point formula, the coordinate of P or P' will be: $(\frac{x+2}{2},\frac{y+4}{2})$ , which is actually at (-7, -2)

Thus.....

$\frac{x+2}{2}=-7\\ \\ x+2=-14\\ \\ x= -16\\ \\ and\\ \\ \frac{y+4}{2}= -2\\ \\ y+4= -4\\ \\ y= -8$

So, the co ordinates of P' is (-7,-2) and Q' is (-16, -8)