Let’s solve each problem step by step. We’ll move the shapes as instructed and find the new coordinates.
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Problem 1a: Triangle with vertices (-1, 0), (-6, -4), and (-2, -5). Move it 4 units up.
When you move a point
up, you add to the
y-coordinate.
- Original point (-1, 0) → move up 4 → y becomes 0 + 4 = 4 → New point:
(-1, 4)
- Original point (-6, -4) → move up 4 → y becomes -4 + 4 = 0 → New point:
(-6, 0)
- Original point (-2, -5) → move up 4 → y becomes -5 + 4 = -1 → New point:
(-2, -1)
✔ New coordinates:
(-1, 4), (-6, 0), (-2, -1)
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Problem 1b: Trapezoid with vertices (-7, 1), (1, 1), (1, -4), and (-6, -4). Move it 1 unit up.
Again, moving up means adding to the y-coordinate.
- (-7, 1) → 1 + 1 = 2 →
(-7, 2)
- (1, 1) → 1 + 1 = 2 →
(1, 2)
- (1, -4) → -4 + 1 = -3 →
(1, -3)
- (-6, -4) → -4 + 1 = -3 →
(-6, -3)
✔ New coordinates:
(-7, 2), (1, 2), (1, -3), (-6, -3)
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Problem 2a: Pentagon with vertices (-10, 2), (-4, 3), (3, 3), (1, -4), and (-7, -5). Move it 6 units up.
Add 6 to each y-coordinate.
- (-10, 2) → 2 + 6 = 8 →
(-10, 8)
- (-4, 3) → 3 + 6 = 9 →
(-4, 9)
- (3, 3) → 3 + 6 = 9 →
(3, 9)
- (1, -4) → -4 + 6 = 2 →
(1, 2)
- (-7, -5) → -5 + 6 = 1 →
(-7, 1)
✔ New coordinates:
(-10, 8), (-4, 9), (3, 9), (1, 2), (-7, 1)
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Problem 2b: Triangle with vertices (2, 0), (4, 6), and (2, 2). Move it 6 units left and 3 units down.
Moving
left means subtract from the
x-coordinate.
Moving
down means subtract from the
y-coordinate.
So for each point:
- Subtract 6 from x
- Subtract 3 from y
First point: (2, 0)
→ x: 2 - 6 = -4
→ y: 0 - 3 = -3
→ New point:
(-4, -3)
Second point: (4, 6)
→ x: 4 - 6 = -2
→ y: 6 - 3 = 3
→ New point:
(-2, 3)
Third point: (2, 2)
→ x: 2 - 6 = -4
→ y: 2 - 3 = -1
→ New point:
(-4, -1)
✔ New coordinates:
(-4, -3), (-2, 3), (-4, -1)
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Final Answer:
1a. (-1, 4), (-6, 0), (-2, -1)
1b. (-7, 2), (1, 2), (1, -3), (-6, -3)
2a. (-10, 8), (-4, 9), (3, 9), (1, 2), (-7, 1)
2b. (-4, -3), (-2, 3), (-4, -1)
Parent Tip: Review the logic above to help your child master the concept of coordinate algebra unit 1 worksheet.
