If the coordinates of the vertices of a triangle are (1, 1), (4, 5), and (7, 2),

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Question: If the coordinates of the vertices of a triangle are (1, 1), (4, 5), and (7, 2), what is the perimeter of the triangle?

Options:

Correct Answer: 14

Solution:

Calculate distances AB, BC, CA and sum them: AB = 5, BC = 5, CA = 7. Perimeter = 5 + 5 + 7 = 17.

If the coordinates of the vertices of a triangle are (1, 1), (4, 5), and (7, 2), what is the perimeter of the triangle?

If the coordinates of the vertices of a triangle are (1, 1), (4, 5), and (7, 2), what is the perimeter of the triangle?

Correct Answer: 17

Step 1: Identify the coordinates of the vertices of the triangle. They are A(1, 1), B(4, 5), and C(7, 2).
Step 2: Calculate the distance between points A and B using the distance formula: AB = √((x2 - x1)² + (y2 - y1)²). Here, (x1, y1) = (1, 1) and (x2, y2) = (4, 5).
Step 3: Plug in the values: AB = √((4 - 1)² + (5 - 1)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.
Step 4: Calculate the distance between points B and C using the same formula: BC = √((7 - 4)² + (2 - 5)²).
Step 5: Plug in the values: BC = √((7 - 4)² + (2 - 5)²) = √(3² + (-3)²) = √(9 + 9) = √18 = 3√2 (approximately 4.24).
Step 6: Calculate the distance between points C and A: CA = √((1 - 7)² + (1 - 2)²).
Step 7: Plug in the values: CA = √((-6)² + (-1)²) = √(36 + 1) = √37 (approximately 6.08).
Step 8: Now, sum the distances to find the perimeter: Perimeter = AB + BC + CA = 5 + 4.24 + 6.08.
Step 9: Calculate the total: Perimeter ≈ 5 + 4.24 + 6.08 = 15.32.

Distance Formula – The distance between two points (x1, y1) and (x2, y2) is calculated using the formula √((x2 - x1)² + (y2 - y1)²).
Perimeter Calculation – The perimeter of a triangle is the sum of the lengths of its sides.