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

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

Options:

Correct Answer: 3

Solution:

Base AB = √((4-1)² + (6-2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

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

If the coordinates of the vertices of a triangle are A(1, 2), B(4, 6), and C(1, 6), what is the base of the triangle 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 base 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 base 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).
Triangle Properties – Understanding the properties of triangles, including the identification of sides and vertices.