Question

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

Step2: Substitute values

Substitute the values into the formula: $d(A,B)=\sqrt{(1 - 1)^2+(5-(-6))^2}=\sqrt{0+(5 + 6)^2}=\sqrt{11^2}$.

Step3: Simplify

$\sqrt{11^2}=11$.

Answer:

$11$