Let’s solve each problem step by step.
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Problem 1: Translate the trapezoid ABCD 5 units to the right.
First, we need to find the original coordinates of points A, B, C, and D from the graph.
Looking at the grid:
- Point A is at (1, 2)
- Point B is at (2, 5)
- Point C is at (1, 7)
- Point D is at (-2, 6)
To translate 5 units to the right, we add 5 to the x-coordinate of each point. The y-coordinates stay the same.
New coordinates:
- A’ = (1 + 5, 2) = (6, 2)
- B’ = (2 + 5, 5) = (7, 5)
- C’ = (1 + 5, 7) = (6, 7)
- D’ = (-2 + 5, 6) = (3, 6)
✔ Checked: All x-values increased by 5, y-values unchanged. Correct.
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Problem 2: Translate the quadrilateral EFGH 7 units upward.
Find original coordinates from the graph:
- E is at (6, -2)
- F is at (8, 1)
- G is at (10, 3)
- H is at (12, 0)
To translate 7 units up, we add 7 to the y-coordinate of each point. X-coordinates stay the same.
New coordinates:
- E’ = (6, -2 + 7) = (6, 5)
- F’ = (8, 1 + 7) = (8, 8)
- G’ = (10, 3 + 7) = (10, 10)
- H’ = (12, 0 + 7) = (12, 7)
✔ Checked: All y-values increased by 7, x-values unchanged. Correct.
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Problem 3: Rectangle MATH — M(-7, -1), A(-3, -1), T(-3, 3). Find coordinate of H.
In a rectangle, opposite sides are equal and parallel. Also, the fourth vertex can be found by matching x and y values.
We have:
- M(-7, -1)
- A(-3, -1) → same y as M, so MA is horizontal.
- T(-3, 3) → same x as A, so AT is vertical.
So, from M(-7, -1), moving up to match T’s y-value (3), we get H.
Or, from T(-3, 3), moving left to match M’s x-value (-7), we get H.
So H must be at (-7, 3).
Check: In rectangle MATH, order matters. Assuming it's labeled in order M→A→T→H→M.
From M to A: right 4 units
From A to T: up 4 units
From T to H: left 4 units → (-3 -4, 3) = (-7, 3)
From H to M: down 4 units → (-7, 3-4) = (-7, -1) → matches M.
✔ So H is at (-7, 3)
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Problem 4: Translate rectangle MATH 3 units downward and 4 units to the right. Find new coordinates.
Original coordinates:
- M(-7, -1)
- A(-3, -1)
- T(-3, 3)
- H(-7, 3) ← from Problem 3
Translation: +4 to x, -3 to y.
New coordinates:
- M’ = (-7 + 4, -1 - 3) = (-3, -4)
- A’ = (-3 + 4, -1 - 3) = (1, -4)
- T’ = (-3 + 4, 3 - 3) = (1, 0)
- H’ = (-7 + 4, 3 - 3) = (-3, 0)
✔ Checked: All x increased by 4, all y decreased by 3. Correct.
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Final Answer:
1. A'(6,2), B'(7,5), C'(6,7), D'(3,6)
2. E'(6,5), F'(8,8), G'(10,10), H'(12,7)
3. H(-7,3)
4. M'(-3,-4), A'(1,-4), T'(1,0), H'(-3,0)
Parent Tip: Review the logic above to help your child master the concept of translations practice worksheet.
