How to Use the Distance Formula to Solve Right Triangles
If you design video games, houses, bridges or just need to mount some shelves, you will often need to calculate the distance between two points. And to do it, you will need to know how to use the distance formula. If you are a math student you will also use the distance formula to solve right triangle problems. Teachers assign these problems so their students will be prepared to take high school exit and college entrance exams. And that's because these tests have right triangle problems, like the one explained here. This example shows you how to find the perimeter of a right triangle with the distance formula.
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Instructions
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Draw a right triangle on graph paper. First, plot the three vertices of the right triangle. Plot point A at the x, y coordinate location (0,0), plot point B at the x, y coordinate location (3, 0), and plot point C at the x, y coordinate location (3, 4). Draw straight lines between points A and B, points B and C, and points C and A. The connected lines form a right triangle.
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Calculate the length of line AB. To use the distance formula to calculate the length of line AB, the difference between the x-coordinate values of the B coordinate must be subtracted from the x-coordinate values of the A coordinate. Since the x-coordinate of point B is 3 and the x-coordinate of point A is 0, the difference between these coordinates is 3 minus 0, or 3.
This value, that is the difference between the x-coordinates, must next be squared. The square of the number can be calculated by multiplying the number by itself. Since the difference between the x-coordinates is 3, the square of the difference is 3 times 3, or 9.
Also the difference between the y-coordinate values of the B coordinate must be subtracted from the y-coordinate values of the A coordinate. Since the y-coordinate of point B is 0 and the y-coordinate of point A is 0, the difference between these coordinates is 0 minus 0, or 0.
This value, that is the difference between the y-coordinates, must next be squared. Since the difference between the y-coordinates is 0, the square of the difference is 0 times 0 or 0.
Sum the squares of the x-difference and the y-differences. Since the square of the x-differences is 9 and the square of the y-differences is 0, the sum of the squares is 9 plus 0 or 9.
Next, take the square root of the sum of the x and y difference squares. The square root of a number is a number that when multiplied by itself is the original number. Since 9 is the sum of the x and y difference squares, the square root of the sums of the difference squares is 3, since 3 times 3 is 9. So the length of line AB of the right triangle is 3.
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Calculate the length of line BC. Follow the distance formula calculation steps in the second step. The result for this example will be 4. In other words, the length of line BC will be 4 units.
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Calculate the length of line CA. Follow the distance formula calculation steps in the second step. The result for this example will be 5. In other words, the length of line CA will be 5 units.
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Calculate the perimeter of the right triangles. The perimeter of a right triangle is equal to the sum of the individual length of its sides. For this example, the lengths of the right triangle sides are 3, 4 and 5. Since 3 + 4 + 5 = 12, the perimeter of the right triangle is 12 units.
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- Photo Credit one side of triangle image by timur1970 from Fotolia.com
