What is the distances for (5,3) and (-1,-5) ?

1 Answer
Ms. Worth
Apr 22, 2018

The distance between those points is #10#

Explanation:

The distance between these two points can be drawn as the hypotenuse of a right triangle.

The legs of this triangle are the lengths of the vertical and horizontal lines that you can draw to meet each other.

The distance along the #x# axis is the distance between the two #x# points #5# and #-1#
#5 - (-1)# = the horizontal distance between the points
That is a distance of #6# points.

The vertical distance up the #y# axis is the difference between the two #y# values, namely #3 - (-5)#, which is a distance of #8#.

These are the legs of the right triangle you can draw to find the length of the hypotenuse.

The Pythagorean Theorem states that
#a^2 + b^2 = c^2#
#6^2 + 8^2 = c^2#

Since these sides form a #3#-#4#-#5# right triangle, then the length of the hypotenuse must be #10.#

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