If the coordinates of the vertices of a triangle are A(1, 2), B(4, 6), and C(7,

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Question: If the coordinates of the vertices of a triangle are A(1, 2), B(4, 6), and C(7, 2), what is the perimeter of the triangle?

Options:

Correct Answer: 14

Solution:

Perimeter = AB + BC + CA = √((4-1)² + (6-2)²) + √((7-4)² + (2-6)²) + √((1-7)² + (2-2)²) = 3 + 5 + 6 = 14.

If the coordinates of the vertices of a triangle are A(1, 2), B(4, 6), and C(7, 2), what is the perimeter of the triangle?

If the coordinates of the vertices of a triangle are A(1, 2), B(4, 6), and C(7, 2), what is the perimeter of the triangle?

Step 1: Identify the coordinates of the vertices of the triangle. They are A(1, 2), B(4, 6), 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, 2) and (x2, y2) = (4, 6).
Step 3: Substitute the values into the formula: AB = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.
Step 4: Calculate the distance between points B and C using the same distance formula: BC = √((7 - 4)² + (2 - 6)²).
Step 5: Substitute the values: BC = √((7 - 4)² + (2 - 6)²) = √(3² + (-4)²) = √(9 + 16) = √25 = 5.
Step 6: Calculate the distance between points C and A: CA = √((1 - 7)² + (2 - 2)²).
Step 7: Substitute the values: CA = √((-6)² + (0)²) = √(36 + 0) = √36 = 6.
Step 8: Add the lengths of all sides to find the perimeter: Perimeter = AB + BC + CA = 5 + 5 + 6.
Step 9: Calculate the total: Perimeter = 16.

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.