If the coordinates of the vertices of a triangle are (1, 2), (3, 4), and (5, 2),

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Question: If the coordinates of the vertices of a triangle are (1, 2), (3, 4), and (5, 2), what is the perimeter of the triangle?

Options:

Correct Answer: 10

Solution:

Perimeter = AB + BC + CA = √[(3-1)² + (4-2)²] + √[(5-3)² + (2-4)²] + √[(1-5)² + (2-2)²] = 2.83 + 2.83 + 4 = 10.

If the coordinates of the vertices of a triangle are (1, 2), (3, 4), and (5, 2), what is the perimeter of the triangle?

If the coordinates of the vertices of a triangle are (1, 2), (3, 4), and (5, 2), what is the perimeter of the triangle?

Step 1: Identify the coordinates of the triangle's vertices. They are A(1, 2), B(3, 4), and C(5, 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, 2) and (x2, y2) = (3, 4).
Step 3: Substitute the values into the formula: AB = √[(3 - 1)² + (4 - 2)²] = √[2² + 2²] = √[4 + 4] = √8 = 2.83.
Step 4: Calculate the distance between points B and C using the same distance formula: BC = √[(5 - 3)² + (2 - 4)²].
Step 5: Substitute the values: BC = √[(5 - 3)² + (2 - 4)²] = √[2² + (-2)²] = √[4 + 4] = √8 = 2.83.
Step 6: Calculate the distance between points C and A: CA = √[(1 - 5)² + (2 - 2)²].
Step 7: Substitute the values: CA = √[(-4)² + (0)²] = √[16 + 0] = √16 = 4.
Step 8: Add all the distances together to find the perimeter: Perimeter = AB + BC + CA = 2.83 + 2.83 + 4 = 10.

Distance Formula – The question tests the understanding of the distance formula to calculate the lengths of the sides of a triangle given its vertices.
Perimeter Calculation – It assesses the ability to sum the lengths of the sides to find the perimeter of the triangle.