In problems below, (a) identify the independent variable and the dependent variable of each equation (use 't' for the independen
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The equation to derive the distance d is . The lengths of the other legs of the given triangle are (y2 - y1) and (x2 - x1).
Consider the two points (x1, y1) and (x2, y2)
The formula used for calculating the distance between the two points is
distance =
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,
And the lengths of the other two legs of the given triangle are,
Length of the adjacent side: (x1, y1) to (x2,y1)
=
=
=
Length of the opposite side: (x2, y1) to (x2, y2)
=
=
=
Therefore, the derived distances for the given triangle are:
, (x2 - x1), and (y2 - y1).
Learn more about the distance between two points here:
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