How do use the pythagorean theorem to find the distance between two points like the points (1,3) and (4,3)?

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Answer 1 · 2016-03-02T14:47:51

The distance between the points is 3

Tony B

Let the distance between points be #d# then

Let #(x_1,y_1) -> (1,3)#
Let #(x_2,y_2)->(4,3)#

Then by Pythagoras

#d^2 =(x_2-x_1)^2+(y_2-y_1)^2#

#d^2=(4-1)^2+(3-3)^2#

Notice that #y_1=y_2# which means that the line between the points is parallel to the x-axis as there is no change in height (y-axis).

#color(brown)("However, the Pythagoras theorem will still work")#

#d^2=3^2+0^2#

#sqrt(d^2)=sqrt(3^2)#

#d=3#