If Point A Is (4, –1) And Point B Is (3, 5), What Is The Square Of The Distance AB² Between Them?

If point A is (4, –1) and point B is (3, 5), what is the square of the distance AB² between them?

Explanation

To find the square of the distance between two points $A(x_1, y_1)$ and $B (x_{2}, y_{2})$ :

$A B^^{2} = (x_{2} - x_{1})^^{2} + (y_{2} - y_{1})^^{2}$ $= (3 - 4)^2 + (5 - (-1))^2 = (-1)^2 + (6)^2 = 1 + 36 = 37$

$= (- 1)^^{2} + (6)^^{2}$

$= 1 + 36$

$= 37$

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