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Holiday Coordinate Polygons Answers
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Holiday Coordinate Polygons Answers
🎄 Part 1: Christmas Tree Polygon
1. Plot and connect the points to form a Christmas tree: A(0, 8), B(-2, 6), C(-3, 4), D(-1, 4), E(-2, 2), F(2, 2), G(1, 4), H(3, 4), I(2, 6)
Answer: Triangle shape with base from (-3, 4) to (3, 4) and peak at (0, 8)
2. What type of polygon is formed?
Answer: Nonagon (9-sided polygon)
3. Calculate the perimeter of the tree polygon.
Solution:
AB = √[(0-(-2))² + (8-6)²] = √[4 + 4] = √8 = 2√2 ≈ 2.83 units
BC = √[(-2-(-3))² + (6-4)²] = √[1 + 4] = √5 ≈ 2.24 units
CD = √[(-3-(-1))² + (4-4)²] = √[4 + 0] = 2 units
DE = √[(-1-(-2))² + (4-2)²] = √[1 + 4] = √5 ≈ 2.24 units
EF = √[(-2-2)² + (2-2)²] = √[16 + 0] = 4 units
FG = √[(2-1)² + (2-4)²] = √[1 + 4] = √5 ≈ 2.24 units
GH = √[(1-3)² + (4-4)²] = √[4 + 0] = 2 units
HI = √[(3-2)² + (4-6)²] = √[1 + 4] = √5 ≈ 2.24 units
IA = √[(2-0)² + (6-8)²] = √[4 + 4] = √8 = 2√2 ≈ 2.83 units
Perimeter = 4 + 4√2 + 4√5 ≈ 20.86 units
AB = √[(0-(-2))² + (8-6)²] = √[4 + 4] = √8 = 2√2 ≈ 2.83 units
BC = √[(-2-(-3))² + (6-4)²] = √[1 + 4] = √5 ≈ 2.24 units
CD = √[(-3-(-1))² + (4-4)²] = √[4 + 0] = 2 units
DE = √[(-1-(-2))² + (4-2)²] = √[1 + 4] = √5 ≈ 2.24 units
EF = √[(-2-2)² + (2-2)²] = √[16 + 0] = 4 units
FG = √[(2-1)² + (2-4)²] = √[1 + 4] = √5 ≈ 2.24 units
GH = √[(1-3)² + (4-4)²] = √[4 + 0] = 2 units
HI = √[(3-2)² + (4-6)²] = √[1 + 4] = √5 ≈ 2.24 units
IA = √[(2-0)² + (6-8)²] = √[4 + 4] = √8 = 2√2 ≈ 2.83 units
Perimeter = 4 + 4√2 + 4√5 ≈ 20.86 units
⭐ Part 2: Star Polygon
4. Plot and connect the points to form a star: J(0, 4), K(-2, 1), L(-4, 1), M(-1, -1), N(-2, -4), O(0, -2), P(2, -4), Q(1, -1), R(4, 1), S(2, 1)
Answer: Five-pointed star shape centered near the origin
5. How many sides does this star polygon have?
Answer: 10 sides (decagon)
6. Calculate the perimeter of the star.
Solution:
JK = √[(0-(-2))² + (4-1)²] = √[4 + 9] = √13 ≈ 3.61 units
KL = √[(-2-(-4))² + (1-1)²] = √[4 + 0] = 2 units
LM = √[(-4-(-1))² + (1-(-1))²] = √[9 + 4] = √13 ≈ 3.61 units
MN = √[(-1-(-2))² + (-1-(-4))²] = √[1 + 9] = √10 ≈ 3.16 units
NO = √[(-2-0)² + (-4-(-2))²] = √[4 + 4] = √8 = 2√2 ≈ 2.83 units
OP = √[(0-2)² + (-2-(-4))²] = √[4 + 4] = √8 = 2√2 ≈ 2.83 units
PQ = √[(2-1)² + (-4-(-1))²] = √[1 + 9] = √10 ≈ 3.16 units
QR = √[(1-4)² + (-1-1)²] = √[9 + 4] = √13 ≈ 3.61 units
RS = √[(4-2)² + (1-1)²] = √[4 + 0] = 2 units
SJ = √[(2-0)² + (1-4)²] = √[4 + 9] = √13 ≈ 3.61 units
Perimeter = 4 + 4√2 + 2√10 + 4√13 ≈ 30.42 units
JK = √[(0-(-2))² + (4-1)²] = √[4 + 9] = √13 ≈ 3.61 units
KL = √[(-2-(-4))² + (1-1)²] = √[4 + 0] = 2 units
LM = √[(-4-(-1))² + (1-(-1))²] = √[9 + 4] = √13 ≈ 3.61 units
MN = √[(-1-(-2))² + (-1-(-4))²] = √[1 + 9] = √10 ≈ 3.16 units
NO = √[(-2-0)² + (-4-(-2))²] = √[4 + 4] = √8 = 2√2 ≈ 2.83 units
OP = √[(0-2)² + (-2-(-4))²] = √[4 + 4] = √8 = 2√2 ≈ 2.83 units
PQ = √[(2-1)² + (-4-(-1))²] = √[1 + 9] = √10 ≈ 3.16 units
QR = √[(1-4)² + (-1-1)²] = √[9 + 4] = √13 ≈ 3.61 units
RS = √[(4-2)² + (1-1)²] = √[4 + 0] = 2 units
SJ = √[(2-0)² + (1-4)²] = √[4 + 9] = √13 ≈ 3.61 units
Perimeter = 4 + 4√2 + 2√10 + 4√13 ≈ 30.42 units
🎁 Part 3: Reflection Questions
7. Which polygon has the larger perimeter and by how much?
Answer: The star polygon has the larger perimeter by approximately 9.56 units (30.42 - 20.86 = 9.56 units)
8. Explain how you would find the area of the Christmas tree polygon.
Answer: Use the Shoelace formula or divide the polygon into triangles and rectangles, then calculate the area of each section and add them together. The irregular shape makes direct calculation challenging.
9. If you moved the star 3 units right and 2 units up, what would be the coordinates of point J?
Answer: J would move from (0, 4) to (3, 6)
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