Question

example 5 rotations
parallelogram fghj has vertices f(2, 1), g(7, 1), h(6, - 3), and j(1, - 3). what are the coordinates of the vertices of its image after a rotation of 180° about the origin?
predict graph parallelogram fghj.
before performing the rotation, predict your results.
to rotate a point 180° counterclockwise about the origin, multiply the x - and y - coordinates by - 1. find the coordinates of the vertices of the image.
(x, y)→(-x, -y)
f(2, 1)→f(_, _)
g(7, 1)→g(_, _)
h(6, - 3)→h(_, _)
j(1, - 3)→j(_, _)
check the image meets the prediction.
check
quadrilateral jklm has coordinates j(1, 2), k(4, 3), l(6, 1), and m(3, 1). determine the coordinates of the vertices of the image after a 270° rotation about the origin.
a. j(2, - 1), k(3, - 4), l(1, - 6), and m(1, - 3)
b. j(2, 1), k(3, 4), l(1, 6), and m(1, 3)
c. j(- 2, 1), k(- 3, 4), l(- 1, 6), and m(- 1, 3)
d. j(- 2, - 1), k(- 3, - 4), l(- 1, - 6), and m(- 1, - 3)

Explanation:

Step1: Recall 270 - degree rotation rule

A 270 - degree counter - clockwise rotation about the origin has the transformation rule $(x,y)\to(y, - x)$.

Step2: Apply rule to point J(1, 2)

For point $J(1,2)$, using the rule $(x,y)\to(y, - x)$, we get $J'(2,-1)$.

Step3: Apply rule to point K(4, 3)

For point $K(4,3)$, $(x,y)\to(y, - x)$ gives $K'(3,-4)$.

Step4: Apply rule to point L(6, 1)

For point $L(6,1)$, $(x,y)\to(y, - x)$ gives $L'(1,-6)$.

Step5: Apply rule to point M(3, 1)

For point $M(3,1)$, $(x,y)\to(y, - x)$ gives $M'(1,-3)$.

Answer:

A. $J'(2, - 1),K'(3, - 4),L'(1, - 6),M'(1, - 3)$