Question

find the distance d(a,b) between points a and b. a(1, - 3), b(-1, - 10) 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, $x_1 = 1,y_1=-3,x_2=-1,y_2 = - 10$.

Step2: Substitute values

$d(A,B)=\sqrt{(-1 - 1)^2+(-10+3)^2}=\sqrt{(-2)^2+(-7)^2}$.

Step3: Calculate squares

$\sqrt{(-2)^2+(-7)^2}=\sqrt{4 + 49}$.

Step4: Simplify

$\sqrt{4 + 49}=\sqrt{53}$.

Answer:

$\sqrt{53}$