Question

find the distance d(a,b) between points a and b. a(1, - 2), b(-1, - 6) d(a,b)= (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1 = 1,y_1=-2,x_2=-1,y_2 = - 6$.

Step2: Substitute values

Substitute the values into the formula: $d(A,B)=\sqrt{(-1 - 1)^2+(-6+2)^2}$.

Step3: Simplify expressions inside square - root

First, calculate $(-1 - 1)^2=(-2)^2 = 4$ and $(-6 + 2)^2=(-4)^2=16$. Then $d(A,B)=\sqrt{4 + 16}$.

Step4: Calculate final result

$d(A,B)=\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}$.

Answer:

$2\sqrt{5}$