If the coordinates of the vertices of a triangle are (0, 0), (4, 0), and (0, 3),

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Question: If the coordinates of the vertices of a triangle are (0, 0), (4, 0), and (0, 3), what is the perimeter of the triangle?

Options:

Correct Answer: 12

Solution:

The lengths of the sides are 4, 3, and 5 (using the Pythagorean theorem). Therefore, the perimeter = 4 + 3 + 5 = 12.

If the coordinates of the vertices of a triangle are (0, 0), (4, 0), and (0, 3), what is the perimeter of the triangle?

If the coordinates of the vertices of a triangle are (0, 0), (4, 0), and (0, 3), what is the perimeter of the triangle?

Step 1: Identify the coordinates of the triangle's vertices. They are (0, 0), (4, 0), and (0, 3).
Step 2: Calculate the length of the first side between (0, 0) and (4, 0). This is a horizontal line, so the length is 4 - 0 = 4.
Step 3: Calculate the length of the second side between (0, 0) and (0, 3). This is a vertical line, so the length is 3 - 0 = 3.
Step 4: Calculate the length of the third side between (4, 0) and (0, 3) using the Pythagorean theorem. The formula is: length = √((x2 - x1)² + (y2 - y1)²). Here, (x1, y1) = (4, 0) and (x2, y2) = (0, 3). So, length = √((0 - 4)² + (3 - 0)²) = √(16 + 9) = √25 = 5.
Step 5: Add the lengths of all three sides to find the perimeter. Perimeter = 4 + 3 + 5 = 12.

Distance Formula – Understanding how to calculate the lengths of the sides of a triangle using the distance formula or Pythagorean theorem.
Perimeter Calculation – Adding the lengths of all sides to find the perimeter of a triangle.
Coordinate Geometry – Using coordinates to determine the geometric properties of shapes.