If the coordinates of the vertices of a triangle are (1, 1), (4, 1), and (1, 5),

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Question: If the coordinates of the vertices of a triangle are (1, 1), (4, 1), and (1, 5), what is the length of the base?

Options:

Correct Answer: 3

Solution:

The base is the distance between (1, 1) and (4, 1): d = √((4-1)² + (1-1)²) = √9 = 3.

If the coordinates of the vertices of a triangle are (1, 1), (4, 1), and (1, 5), what is the length of the base?

If the coordinates of the vertices of a triangle are (1, 1), (4, 1), and (1, 5), what is the length of the base?

Step 1: Identify the coordinates of the triangle's vertices. They are (1, 1), (4, 1), and (1, 5).
Step 2: Determine which two points will be used to find the base. The base will be between the points (1, 1) and (4, 1).
Step 3: Use the distance formula to calculate the length of the base. The distance formula is d = √((x2 - x1)² + (y2 - y1)²).
Step 4: Plug in the coordinates of the two points into the formula. Here, (x1, y1) = (1, 1) and (x2, y2) = (4, 1).
Step 5: Calculate the difference in the x-coordinates: (4 - 1) = 3.
Step 6: Calculate the difference in the y-coordinates: (1 - 1) = 0.
Step 7: Substitute these values into the distance formula: d = √((3)² + (0)²).
Step 8: Simplify the equation: d = √(9 + 0) = √9.
Step 9: Calculate the square root: √9 = 3.
Step 10: Conclude that the length of the base is 3.

Distance Formula – The distance between two points in a Cartesian plane is calculated using the formula d = √((x2 - x1)² + (y2 - y1)²).
Triangle Properties – Understanding the properties of triangles, including identifying bases and heights.