How can you use the Pythagorean Theorem to figure out the distance between two coordinates?

1 Answer
smendyka · sankarankalyanam
Feb 5, 2018

See a solution explanation below:

Explanation:

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See the image above.

If we want to determine the distance between points #(x_1, y_1)# and #(x_2, y_2)# we can use the Pythagorean Theorem as follows:

Let's call the distance between the two points #d#

Because the lines between #(x_1, y_1)# #(x_2, y_1)# and #(x_2, y_2)# #(x_2, y_1)# form a right triangle. Therefore we can use the distance of the lines to determine the distance of the line between the two points which is the hypotenuse of the right triangle.

The Pythagorean Theorem states:

#d^2 = a^2 + b^2#

The distance between #(x_1, y_1)# #(x_2, y_1)# is #(x_2 - x_1)#

The distance between #(x_2, y_2)# #(x_2, y_1)# is #(y_2 - y_1)#

Substituting and solving for #d# gives:

#d^2 = (x_2 - x^1)^2 + (y_2 - y_1)^2#

#sqrt(d^2) = sqrt((x_2 - x^1)^2 + (y_2 - y_1)^2)#

#d = sqrt((x_2 - x^1)^2 + (y_2 - y_1)^2)#

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