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

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

Options:

Correct Answer: 4

Solution:

Using the distance formula, AB = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.

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

If the coordinates of the vertices of triangle ABC are 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 (x2 - x1) which is (4 - 1) = 3.
Step 5: Calculate (y2 - y1) which is (6 - 2) = 4.
Step 6: Square the results from Step 4 and Step 5. So, (3)² = 9 and (4)² = 16.
Step 7: Add the squared results together: 9 + 16 = 25.
Step 8: Take the square root of the sum from Step 7: √25 = 5.
Step 9: 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 and calculate distances in a Cartesian coordinate system.