What is the ordered pair of X′ after point X (3, 4) is rotated 180°?

Question

What is the ordered pair of X′ after point X (3, 4) is rotated 180°?

1.  X′ (3, −4) 
2. X′ (−3, −4) 
3. X′ (−4, 3) 
4. X′ (−4, −3)

Answer 1

The correct answer choice is (2).

Rotating a point (about the origin) transforms (x,y) into (-x,-y).

We presume the rotation was to be made around the origin since it was not otherwise specified.

Answer 2

To solve this problem, first graph the point. Then think of the line segment that connects that point to the origin (0,0).

Now think of rotating that line segment about the origin by 180 degrees. Where would the other end of the line segment end up?