To solve this problem, we need to find the perimeter of each shape by calculating the distance between consecutive points and then adding those distances together.
We’ll use the
distance formula between two points (x₁, y₁) and (x₂, y₂):
> Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
But since many of these shapes are on a grid with horizontal or vertical sides, we can often just count units — that’s easier!
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Let’s go one by one.
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Problem A: A(1, 3), B(5, 3), C(5, 0), D(1, 0)
Plotting these:
- From A to B: same y, x goes from 1 to 5 → 4 units right
- From B to C: same x, y goes from 3 to 0 → 3 units down
- From C to D: same y, x goes from 5 to 1 → 4 units left
- From D to A: same x, y goes from 0 to 3 → 3 units up
So it’s a rectangle: 4 + 3 + 4 + 3 =
14 units
✔ Perimeter for A:
14 units
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Problem B: P(-2, 4), Q(2, 4), R(2, 1), S(-2, 1)
Same pattern:
- P to Q: x from -2 to 2 → 4 units
- Q to R: y from 4 to 1 → 3 units
- R to S: x from 2 to -2 → 4 units
- S to P: y from 1 to 4 → 3 units
Again, rectangle: 4 + 3 + 4 + 3 =
14 units
✔ Perimeter for B:
14 units
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Problem C: E(-4, 6), F(4, 6), G(4, -2), H(-4, -2)
- E to F: x from -4 to 4 → 8 units
- F to G: y from 6 to -2 → 8 units
- G to H: x from 4 to -4 → 8 units
- H to E: y from -2 to 6 → 8 units
Wait — all sides are 8? That’s a square!
Perimeter = 8 × 4 =
32 units
✔ Perimeter for C:
32 units
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Problem D: J(-3, -3), K(3, -3), L(3, 3), M(-3, 3)
- J to K: x from -3 to 3 → 6 units
- K to L: y from -3 to 3 → 6 units
- L to M: x from 3 to -3 → 6 units
- M to J: y from 3 to -3 → 6 units
Another square! Side length 6.
Perimeter = 6 × 4 =
24 units
✔ Perimeter for D:
24 units
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Double-checking:
All shapes are rectangles or squares aligned with axes → no diagonals → easy to calculate by counting horizontal/vertical segments.
Final answers:
A: 14
B: 14
C: 32
D: 24
Final Answer:
A: 14 units, B: 14 units, C: 32 units, D: 24 units
Parent Tip: Review the logic above to help your child master the concept of perimeter and area in the coordinate plane worksheet.
