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

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Question: If the coordinates of the vertices of a triangle are A(1, 1), B(4, 5), and C(7, 2), what is the length of side AB?

Options:

Correct Answer: 5

Solution:

Length AB = √((4 - 1)² + (5 - 1)²) = √(9 + 16) = √25 = 5.

If the coordinates of the vertices of a triangle are A(1, 1), B(4, 5), and C(7, 2), what is the length of side AB?

If the coordinates of the vertices of a triangle are A(1, 1), B(4, 5), and C(7, 2), what is the length of side AB?

Step 1: Identify the coordinates of points A and B. A is at (1, 1) and B is at (4, 5).
Step 2: Use the distance formula to find the length of side AB. The formula is Length = √((x2 - x1)² + (y2 - y1)²).
Step 3: Substitute the coordinates of A and B into the formula. Here, x1 = 1, y1 = 1, x2 = 4, and y2 = 5.
Step 4: Calculate (x2 - x1) which is (4 - 1) = 3.
Step 5: Calculate (y2 - y1) which is (5 - 1) = 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) in a Cartesian plane is calculated using the formula √((x2 - x1)² + (y2 - y1)²).
Coordinate Geometry – Understanding how to work with coordinates and apply geometric principles to find lengths and distances.