Question

Find the distance between the two points in simplest radical form.(6,−1) and (−2,−9)

Answer 1

Answer:
`8√(2)`

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Work Shown:

`(x_1,y_1) = (6,-1) \text{ and } (x_2, y_2) = (-2,-9)\\\\d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((6-(-2))^2 + (-1-(-9))^2)\\\\d = √((6+2)^2 + (-1+9)^2)\\\\d = √((8)^2 + (8)^2)\\\\d = √(64 + 64)\\\\d = √(128)\\\\d = √(64*2)\\\\d = √(64)*√(2)\\\\d = 8√(2)`

I used the distance formula. A slight alternative is to plot the points to form a right triangle, then apply the pythagorean theorem.