Question

solve the problems below. show all work. a. triangle def is translated 3 units to the left and 5 units up to create triangle def. what rule describes this transformation? c. trapezoid ghj k was translated 2 units to the left and 3 units up! what rule describes this transformation? e. trapezoid klmn is rotated 90° clockwise about the origin to create trapezoid klmn. what rule describes this transformation? b. trapezoid klmn is rotate d. parallelogram pq to the right and 3 ur describes this transf f. parallelogram a

Explanation:

Step1: Recall translation rule

In a coordinate - plane, a translation of $a$ units to the left and $b$ units up for a point $(x,y)$ is given by the rule $(x,y)\to(x - a,y + b)$.

Step2: Solve for part A

For triangle DEF translated 3 units to the left and 5 units up, the rule is $(x,y)\to(x-3,y + 5)$.

Step3: Solve for part C

For trapezoid GHJ K translated 2 units to the left and 3 units up, the rule is $(x,y)\to(x - 2,y+3)$.

Step4: Recall rotation rule

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

Step5: Solve for part E

For trapezoid KLMN rotated 90 degrees clockwise about the origin, the rule is $(x,y)\to(y,-x)$.

Answer:

A. $(x,y)\to(x - 3,y + 5)$
C. $(x,y)\to(x - 2,y+3)$
E. $(x,y)\to(y,-x)$