How do you find the distance between (–3, –2) and (1, 4)?

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Answer 1 · 2015-07-01T21:38:17

#D = 2.sqrt(13)#

The distance between two points A(x;y) and B(x';y') can be calculate with the formula :

#D = sqrt((x'-x)^2+(y'-y)^2)#

Then for : A(-3;-2) and B(1;4) we have :

#D = sqrt((1-(-3))^2+(4-(-2))^2)#

#D= sqrt(4^2 + 6^2)#

#D = sqrt(16+36) = sqrt(52) = 2.sqrt(13)#

The distance between A(-3;-2) and B(1;4) is exactly #2.sqrt(13)#

Why this formula work ? In fact, we only calculate the length of vector(BA), and we implicitly use the Pythagorean theorem on it.