Question

the letter shows the coordinates of a rectangle that has been rotated about the origin. pre - image: h(-7, -8), i(-7, -3), j(-2, -8), k(-2, -3). image: h(-8, 7), i(-3, 7), j(-8, 2), k(-3, 2). the rectangle was rotated _ degrees clockwise about the origin and the algebraic rule is _

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree clockwise rotation about the origin is $(x,y)\to(y, - x)$.

Step2: Apply rule to point K(-2,-3)

For point K(-2,-3), using the rule $(x,y)\to(y, - x)$, we get $x=-2,y = - 3$, and the new coordinates are $(-3,2)$.

Step3: Apply rule to point J(-2,-8)

For point J(-2,-8), with $x=-2,y=-8$, the new coordinates are $(-8,2)$ according to the rule $(x,y)\to(y, - x)$.

Step4: Apply rule to point I(-7,-3)

For point I(-7,-3), when $x = - 7,y=-3$, the new coordinates are $(-3,7)$ using the rule $(x,y)\to(y, - x)$.

Step5: Apply rule to point H(-7,-8)

For point H(-7,-8), with $x=-7,y=-8$, the new coordinates are $(-8,7)$ by the rule $(x,y)\to(y, - x)$.

Answer:

The rotation is 90 degrees clockwise and the algebraic rule is $(x,y)\to(y, - x)$