Question

find the distance d(a,b) between points a and b. a(6,5); b(-4,-1) 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, $x_1 = 6,y_1 = 5,x_2=-4,y_2=-1$.

Step2: Substitute values

$d(A,B)=\sqrt{(-4 - 6)^2+(-1 - 5)^2}=\sqrt{(-10)^2+(-6)^2}$.

Step3: Calculate squares

$d(A,B)=\sqrt{100 + 36}$.

Step4: Simplify

$d(A,B)=\sqrt{136}=\sqrt{4\times34}=2\sqrt{34}$.

Answer:

$2\sqrt{34}$