Question

question 1 - 3
δabc has vertices a(-2, 1), b(3, 2) and c(5, -1). what are the coordinates of the vertices of δabc after a rotation of 180° clockwise about the origin?
a(2, -1), b(-3, -2), c(-5, 1)
a(-2, -1), b(-3, -2), c(-5, 1)
a(-2, -1), b(-3, -2), c(-5, -1)
a(2, 1), b(3, 2), c(5, 1)

Explanation:

Step1: Recall rotation rule

The rule for a 180 - degree clockwise rotation about the origin is $(x,y)\to(-x,-y)$.

Step2: Apply rule to point A

For point A(-2, 1), $x=-2,y = 1$. After rotation, $x'=-(-2)=2,y'=-1$, so A' is (2, -1).

Step3: Apply rule to point B

For point B(3, 2), $x = 3,y=2$. After rotation, $x'=-3,y'=-2$, so B' is (-3, -2).

Step4: Apply rule to point C

For point C(5, -1), $x = 5,y=-1$. After rotation, $x'=-5,y'=-(-1)=1$, so C' is (-5, 1).

Answer:

A. A'(2, -1), B'(-3, -2), C'(-5, 1)