Question

1. figure abcd has vertices a(-2, -2), b(1, 1), c(0, 4), and d(-3, 5). the figure is translated 5 units to the right and 6 units down. then it is translated 2 units to the left and 2 units up. what are the coordinates of image a\b\c\d\ after both translations? a\(__, ) b\(, ) c\(, ) d\(, __)

Explanation:

Step1: First translation for x - coordinate of A

Add 5 to the x - coordinate of A(-2, -2).
$-2 + 5=3$

Step2: First translation for y - coordinate of A

Subtract 6 from the y - coordinate of A.
$-2-6 = - 8$

Step3: Second translation for x - coordinate of A

Subtract 2 from the x - coordinate after the first translation.
$3-2 = 1$

Step4: Second translation for y - coordinate of A

Add 2 to the y - coordinate after the first translation.
$-8 + 2=-6$

Step5: First translation for x - coordinate of B

Add 5 to the x - coordinate of B(1, 1).
$1 + 5=6$

Step6: First translation for y - coordinate of B

Subtract 6 from the y - coordinate of B.
$1-6=-5$

Step7: Second translation for x - coordinate of B

Subtract 2 from the x - coordinate after the first translation.
$6-2 = 4$

Step8: Second translation for y - coordinate of B

Add 2 to the y - coordinate after the first translation.
$-5 + 2=-3$

Step9: First translation for x - coordinate of C

Add 5 to the x - coordinate of C(0, 4).
$0 + 5=5$

Step10: First translation for y - coordinate of C

Subtract 6 from the y - coordinate of C.
$4-6=-2$

Step11: Second translation for x - coordinate of C

Subtract 2 from the x - coordinate after the first translation.
$5-2 = 3$

Step12: Second translation for y - coordinate of C

Add 2 to the y - coordinate after the first translation.
$-2+2 = 0$

Step13: First translation for x - coordinate of D

Add 5 to the x - coordinate of D(-3, 5).
$-3 + 5=2$

Step14: First translation for y - coordinate of D

Subtract 6 from the y - coordinate of D.
$5-6=-1$

Step15: Second translation for x - coordinate of D

Subtract 2 from the x - coordinate after the first translation.
$2-2 = 0$

Step16: Second translation for y - coordinate of D

Add 2 to the y - coordinate after the first translation.
$-1 + 2=1$

Answer:

$A''(1,-6)$
$B''(4,-3)$
$C''(3,0)$
$D''(0,1)$