Question

rotations
drag the image coordinates at the right to match
the correct pre - image coordinate.
rotate 180° cc about origin
p(6,7) q(8, - 2) r(3, - 4)
p q r
(-7,-6)
(-3,4)
(8,2)
(-8,2)
(7,6)
(-4,3)
(-2,8)
(-6,-7)

Explanation:

Step1: Recall 180° rotation rule

For a point \((x,y)\) rotated \(180^\circ\) about the origin, the image is \((-x,-y)\).

Step2: Find \(P'\) for \(P(6,7)\)

Apply the rule: \(x = 6\) becomes \(-6\), \(y = 7\) becomes \(-7\). So \(P' = (-6,-7)\).

Step3: Find \(Q'\) for \(Q(8,-2)\)

Apply the rule: \(x = 8\) becomes \(-8\), \(y = -2\) becomes \(2\). So \(Q' = (-8,2)\).

Step4: Find \(R'\) for \(R(3,-4)\)

Apply the rule: \(x = 3\) becomes \(-3\), \(y = -4\) becomes \(4\). So \(R' = (-3,4)\).

Answer:

\(P'\): \((-6,-7)\)
\(Q'\): \((-8,2)\)
\(R'\): \((-3,4)\)