Question

rotations
triangle hop has coordinates h(2,1), o(-3,4), and p(5,7). determine the coordinates of the image of △hop after each rotation.
a rotation 90° clockwise about the origin
a rotation 90° counter - clockwise about the origin
a rotation 180° about the origin
3 fill in the blank 2 points
a.
h ( type your answer_, type your answer_)
o ( type your answer_, type your answer_)
p ( type your answer_, type your answer_)

Explanation:

Step1: Recall 90 - degree clockwise rotation rule

The rule for a 90 - degree clockwise rotation about the origin is $(x,y)\to(y, - x)$.
For point $H(2,1)$:
$H'(1,-2)$
For point $O(-3,4)$:
$O'(4,3)$
For point $P(5,7)$:
$P'(7,-5)$

Step2: Recall 90 - degree counter - clockwise rotation rule

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$.
For point $H(2,1)$:
$H'(-1,2)$
For point $O(-3,4)$:
$O'(-4,-3)$
For point $P(5,7)$:
$P'(-7,5)$

Step3: Recall 180 - degree rotation rule

The rule for a 180 - degree rotation about the origin is $(x,y)\to(-x,-y)$.
For point $H(2,1)$:
$H'(-2,-1)$
For point $O(-3,4)$:
$O'(3,-4)$
For point $P(5,7)$:
$P'(-5,-7)$

Answer:

a.
90 - degree clockwise:
$H'(1,-2)$
$O'(4,3)$
$P'(7,-5)$
90 - degree counter - clockwise:
$H'(-1,2)$
$O'(-4,-3)$
$P'(-7,5)$
180 - degree:
$H'(-2,-1)$
$O'(3,-4)$
$P'(-5,-7)$