Question

rectangle abcd has vertices at a(1,3), b(4,3), c(4,1), and d(1,1). rotate figure abcd 90° counter - clockwise around the origin.

Explanation:

Step1: Recall rotation rule

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

Step2: Apply rule to point A'

For point $A'(1,3)$, using the rule $(x,y)\to(-y,x)$, we get $A''(-3,1)$.

Step3: Apply rule to point B'

For point $B'(4,3)$, using the rule $(x,y)\to(-y,x)$, we get $B''(-3,4)$.

Step4: Apply rule to point C'

For point $C'(4,1)$, using the rule $(x,y)\to(-y,x)$, we get $C''(-1,4)$.

Step5: Apply rule to point D'

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

Answer:

The new vertices of the rotated rectangle are $A''(-3,1), B''(-3,4), C''(-1,4), D''(-1,1)$