Question

find the coordinates of the figure with the given coordinates after the transformation on the plane. pre - image: a(1, 3), b(1, 1), c(4, 1) image: triangle def, rotation of abc 270° counterclockwise about the origin

Explanation:

Step1: Recall rotation rule

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

Step2: Rotate point A

For point $A(1,3)$, applying the rule: $(1,3)\to(3,-1)$. So $D(3,-1)$.

Step3: Rotate point B

For point $B(1,1)$, applying the rule: $(1,1)\to(1,-1)$. So $E(1,-1)$.

Step4: Rotate point C

For point $C(4,1)$, applying the rule: $(4,1)\to(1,-4)$. So $F(1,-4)$.

Answer:

$D(3,-1)$
$E(1,-1)$
$F(1,-4)$