Question

Point Y (-1,-3) is rotated 180° about the origin. What are the coordinates of its image, point Y prime ?

1.Y' (-3,-1)
2.Y' (-3,1)
3.Y' (1,3)
4.Y' (3,-1)

Answer 1

The correct answer is (1,3)

Answer 2

Refer to the figure shown below.

When the point Y (-1,-3) is rotated 180 about O, it sweeps a semicircular arc to the point Y' (1,3).
The radius of the semicircle is

`r = \sqrt{1^(2) + 3^(2)} = √(10) \\ or \\ r = \sqrt{(-1)^(2) + (-3)^(2) } = √(10)`

Answer: 3. Y' (1,3)