If triangle ABC has vertices A(1, 2), B(4, 6), and C(1, 6), what is the length o

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Question: If triangle ABC has vertices A(1, 2), B(4, 6), and C(1, 6), what is the length of side AB?

Options:

Correct Answer: 4.0

Solution:

Using the distance formula: AB = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.0.

If triangle ABC has vertices A(1, 2), B(4, 6), and C(1, 6), what is the length of side AB?

If triangle ABC has vertices A(1, 2), B(4, 6), and C(1, 6), what is the length of side AB?

Step 1: Identify the coordinates of points A and B. A is at (1, 2) and B is at (4, 6).
Step 2: Use the distance formula to find the length of side AB. The distance formula is: distance = √((x2 - x1)² + (y2 - y1)²).
Step 3: Substitute the coordinates of A and B into the formula. Here, x1 = 1, y1 = 2, x2 = 4, and y2 = 6.
Step 4: Calculate the differences: (x2 - x1) = (4 - 1) = 3 and (y2 - y1) = (6 - 2) = 4.
Step 5: Square the differences: (3)² = 9 and (4)² = 16.
Step 6: Add the squared differences: 9 + 16 = 25.
Step 7: Take the square root of the sum: √25 = 5.
Step 8: Conclude that the length of side AB is 5.

Distance Formula – The distance between two points (x1, y1) and (x2, y2) is calculated using the formula √((x2 - x1)² + (y2 - y1)²).
Coordinate Geometry – Understanding how to plot points on a Cartesian plane and calculate distances between them.