Let’s solve each translation problem step by step.
We are given a preimage (original shape) and its translated image (moved shape). We need to describe how the shape moved — specifically, how many units left/right and up/down.
Remember:
- Right = positive x-direction
- Left = negative x-direction
- Up = positive y-direction
- Down = negative y-direction
We’ll pick one point from the preimage and see where it lands in the image. That tells us the whole translation.
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Problem ②:
Preimage triangle PQR → Image triangle P’Q’R’
Pick point P:
Original P is at (-4, -1)
Image P’ is at (-2, 3)
Change in x: from -4 to -2 → that’s +2 (so 2 units right)
Change in y: from -1 to 3 → that’s +4 (so 4 units up)
Check with another point to be sure:
Point Q: original (-5, -3), image Q’ (-3, 1)
x: -5 → -3 = +2
y: -3 → 1 = +4
✔
So translation:
2 units right and 4 units up
Sentence: Triangle PQR was translated 2 units to the right and 4 units up to form triangle P’Q’R’.
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Problem ③:
Preimage rectangle ABCD → Image rectangle A’B’C’D’
Pick point A:
Original A is at (-6, 4)
Image A’ is at (-2, -4)
Change in x: -6 → -2 = +4 (4 units right)
Change in y: 4 → -4 = -8 (8 units down)
Check point B: original (-6, 1), image B’ (-2, -7)
x: -6 → -2 = +4
y: 1 → -7 = -8
✔
Translation:
4 units right and 8 units down
Sentence: Rectangle ABCD was translated 4 units to the right and 8 units down to form rectangle A’B’C’D’.
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Problem ④:
Preimage trapezoid PQRS → Image trapezoid P’Q’R’S’
Pick point P:
Original P is at (2, 5)
Image P’ is at (4, 0)
Change in x: 2 → 4 = +2 (2 units right)
Change in y: 5 → 0 = -5 (5 units down)
Check point Q: original (3, 5), image Q’ (5, 0)
x: 3 → 5 = +2
y: 5 → 0 = -5
✔
Translation:
2 units right and 5 units down
Sentence: Trapezoid PQRS was translated 2 units to the right and 5 units down to form trapezoid P’Q’R’S’.
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Final Answer:
② Triangle PQR was translated 2 units to the right and 4 units up to form triangle P’Q’R’.
③ Rectangle ABCD was translated 4 units to the right and 8 units down to form rectangle A’B’C’D’.
④ Trapezoid PQRS was translated 2 units to the right and 5 units down to form trapezoid P’Q’R’S’.
Parent Tip: Review the logic above to help your child master the concept of translations worksheet math.
