In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2

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Question: In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2) respectively, what is the length of side AB?

Options:

Correct Answer: 5

Solution:

Length of AB = √[(4-1)² + (6-2)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.

In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2) respectively, what is the length of side AB?

In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2) respectively, what is the length of side AB?

Correct Answer: 5

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 formula is: Length = √[(x2 - x1)² + (y2 - y1)²].
Step 3: Substitute the coordinates of A and B into the formula. Here, (x1, y1) = (1, 2) and (x2, y2) = (4, 6).
Step 4: Calculate (x2 - x1) which is (4 - 1) = 3.
Step 5: Calculate (y2 - y1) which is (6 - 2) = 4.
Step 6: Now square both results: (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: √25 = 5.
Step 9: Therefore, the length of side AB is 5.

Distance Formula – The distance between two points in a Cartesian plane is calculated using the formula √[(x2 - x1)² + (y2 - y1)²].
Coordinate Geometry – Understanding how to apply coordinates of points to find lengths and other properties in geometric figures.