Boone Hodges
04/16/2024 · Junior High School
Question Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points, to the nearest tenth (if necessary).
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Step-by-step Solution
To graph a right triangle with the two points forming the hypotenuse, we need to know the coordinates of the two points. Let's denote the coordinates of the first point as \( (x_1, y_1) \) and the coordinates of the second point as \( (x_2, y_2) \).
The distance between the two points can be calculated using the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Let's assume the coordinates of the two points are \( (x_1, y_1) = (0, 0) \) and \( (x_2, y_2) = (3, 4) \). We will calculate the distance between these two points.
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{\left(3-0\right)^{2}+\left(4-0\right)^{2}}\)
- step1: Remove 0:
\(\sqrt{3^{2}+\left(4-0\right)^{2}}\)
- step2: Remove 0:
\(\sqrt{3^{2}+4^{2}}\)
- step3: Add the numbers:
\(\sqrt{25}\)
- step4: Write in exponential form:
\(\sqrt{5^{2}}\)
- step5: Simplify the root:
\(5\)
The distance between the two points is 5 units.
Therefore, the distance between the two points forming the hypotenuse of the right triangle is 5 units.
Quick Answer
The distance between the two points is 5 units.
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