Question

quadrilateral mnpq has vertices m(2, 5), n(6, 4), p(6, 1), and q(2, 1). graph the figure and its image after a counterclockwise rotation of 270° about the origin. then give the coordinates of the vertices for quadrilateral mnpq.

Explanation:

Step1: Recall rotation rule

The rule for a counter - clockwise rotation of 270° about the origin is $(x,y)\to(y, - x)$.

Step2: Find coordinates of $M'$

For point $M(2,5)$, using the rule $(x,y)\to(y, - x)$, we get $M'(5,-2)$.

Step3: Find coordinates of $N'$

For point $N(6,4)$, using the rule $(x,y)\to(y, - x)$, we get $N'(4,-6)$.

Step4: Find coordinates of $P'$

For point $P(6,1)$, using the rule $(x,y)\to(y, - x)$, we get $P'(1,-6)$.

Step5: Find coordinates of $Q'$

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

Answer:

$M'(5,-2),N'(4,-6),P'(1,-6),Q'(1,-2)$