The equation to derive the distance d is $\sqrt{(x2-x1)^2+(y2-y1)^2}$ . 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 = $\sqrt{(x2-x1)^2+(y2-y1)^2}$

<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,

$d = \sqrt{(x2-x1)^2+(y2-y1)^2}$

And the lengths of the other two legs of the given triangle are,

Length of the adjacent side: (x1, y1) to (x2,y1)

= $\sqrt{(x2-x1)^2+(y1-y1)^2}$

= $\sqrt{(x2-x1)^2+0}$

= $(x2-x1)$

Length of the opposite side: (x2, y1) to (x2, y2)

= $\sqrt{(x2-x2)^2+(y2-y1)^2}$

= $\sqrt{0+(y2-y1)^2}$

= $(y2-y1)$

Therefore, the derived distances for the given triangle are:

$d=\sqrt{(x2-x1)^2+(y2-y1)^2}$ , (x2 - x1), and (y2 - y1).

Learn more about the distance between two points here:

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