Question

find the distance d(a,b) between points a and b. a(3, - 1); b(- 6, - 7) 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 $x_1 = 3,y_1=-1,x_2=-6,y_2 = - 7$.

Step2: Substitute values

$d(A,B)=\sqrt{(-6 - 3)^2+(-7+1)^2}=\sqrt{(-9)^2+(-6)^2}$.

Step3: Calculate squares

$\sqrt{(-9)^2+(-6)^2}=\sqrt{81 + 36}$.

Step4: Add values inside square - root

$\sqrt{81+36}=\sqrt{117}$.

Step5: Simplify the square - root

$\sqrt{117}=\sqrt{9\times13}=3\sqrt{13}$.

Answer:

$3\sqrt{13}$