Question

a triangle with vertices at (3, -2),(5, -4),(7, -2) is rotated 180 degrees around the origin. what are the new coordinates of the point (3, -2)?
a. (3,2)
b. (-3, -2)
c. (-3,2)
d. (2, -3)

a figure undergoes a rotation of 90 degrees counterclockwise. how do the coordinates of a point (x, y) change?
a. (-y, -x)
b. (y, x)
c. (-y, x)
d. (x, -y)

Explanation:

Step1: Recall 180 - degree rotation rule

When a point $(x,y)$ is rotated 180 degrees around the origin, the new coordinates are $(-x,-y)$.

Step2: Apply the rule to the point $(3, - 2)$

For the point $(3,-2)$, $x = 3$ and $y=-2$. The new - $x$ value is $-3$ and the new - $y$ value is $-(-2)=2$. So the new coordinates are $(-3,2)$.

Step3: Recall 90 - degree counter - clockwise rotation rule

When a point $(x,y)$ is rotated 90 degrees counter - clockwise around the origin, the new coordinates are $(-y,x)$.

Answer:

1. c. $(-3,2)$
2. c. $(-y,x)$