Question

find the distance d(a,b) between points a and b. a(5,3); b(-2,-1) d(a,b) = (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify distance formula

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

Step2: Substitute coordinates

Here, $x_1 = 5,y_1=3,x_2=-2,y_2 = - 1$. So $d(A,B)=\sqrt{(-2 - 5)^2+(-1 - 3)^2}$.

Step3: Calculate values inside square - root

First, $(-2 - 5)^2=(-7)^2 = 49$ and $(-1 - 3)^2=(-4)^2=16$. Then $d(A,B)=\sqrt{49 + 16}$.

Step4: Simplify

$49+16 = 65$, so $d(A,B)=\sqrt{65}$.

Answer:

$\sqrt{65}$