Question

triangle rst is rotated 90° counterclockwise about the origin. the result is △rst, as shown below. (a) the arrows below show that the coordinates on the left are mapped to the coordinates on the right. fill in the blanks to give the coordinates after the rotation. original coordinates → final coordinates r(-1,3)→r(-3,-1) s(2,6)→s(-6,2) t(0,4)→t(-4,0) (b) choose the general rule below that describes the rotation mapping △rst to △rst. (x,y)→(-y,x) (x,y)→(x,-y) (x,y)→(y,x) (x,y)→(-y,-x) (x,y)→(-x,y) (x,y)→(-x,-y) (x,y)→(y,-x)

Explanation:

Step1: Recall 90 - degree counter - clockwise rotation rule

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

Step2: Apply rule to point R

Given $R(-1,3)$, using the rule $(x,y)\to(-y,x)$, we substitute $x=-1$ and $y = 3$. Then $-y=-3$ and $x=-1$, so $R'(-3,-1)$.

Step3: Apply rule to point S

Given $S(2,6)$, using the rule $(x,y)\to(-y,x)$, we substitute $x = 2$ and $y=6$. Then $-y=-6$ and $x = 2$, so $S'(-6,2)$.

Step4: Apply rule to point T

Given $T(0,4)$, using the rule $(x,y)\to(-y,x)$, we substitute $x = 0$ and $y = 4$. Then $-y=-4$ and $x = 0$, so $T'(-4,0)$.

Step5: Select the general rule

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

Answer:

(a) $R'(-3,-1)$, $S'(-6,2)$, $T'(-4,0)$
(b) $(x,y)\to(-y,x)$