The equation to derive the distance d is
. The lengths of the other legs of the given triangle are (y2 - y1) and (x2 - x1).
<h3>What is the formula for calculating the distance between two points?</h3>
Consider the two points (x1, y1) and (x2, y2)
The formula used for calculating the distance between the two points is
distance = ![\sqrt{(x2-x1)^2+(y2-y1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%7D)
<h3>Calculation:</h3>
Given that,
The triangle in the graph has vertices (x1, y1), (x2, y2), and (x2, y1)
Since this triangle makes 90°, it is a right-angled triangle.
Hypotenuse = (x1, y1) to (x2, y2), Adjacent = (x1, y1) to (x2,y1), and Opposite = (x2, y1) to (x2, y2).
Consider the length of the hypotenuse = d
So, using the distance formula, the length of the hypotenuse(d) is,
![d = \sqrt{(x2-x1)^2+(y2-y1)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%7D)
And the lengths of the other two legs of the given triangle are,
Length of the adjacent side: (x1, y1) to (x2,y1)
= ![\sqrt{(x2-x1)^2+(y1-y1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x2-x1%29%5E2%2B%28y1-y1%29%5E2%7D)
= ![\sqrt{(x2-x1)^2+0}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x2-x1%29%5E2%2B0%7D)
= ![(x2-x1)](https://tex.z-dn.net/?f=%28x2-x1%29)
Length of the opposite side: (x2, y1) to (x2, y2)
= ![\sqrt{(x2-x2)^2+(y2-y1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x2-x2%29%5E2%2B%28y2-y1%29%5E2%7D)
= ![\sqrt{0+(y2-y1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B0%2B%28y2-y1%29%5E2%7D)
= ![(y2-y1)](https://tex.z-dn.net/?f=%28y2-y1%29)
Therefore, the derived distances for the given triangle are:
, (x2 - x1), and (y2 - y1).
Learn more about the distance between two points here:
brainly.com/question/661229
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