Question

find the distance d(a,b) between points a and b. a(7, - 5); b(7,1) 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 $x_1 = 7,y_1=-5,x_2 = 7,y_2 = 1$.

Step2: Substitute values

Substitute the values into the formula: $d(A,B)=\sqrt{(7 - 7)^2+(1-(-5))^2}=\sqrt{0+(1 + 5)^2}=\sqrt{6^2}$.

Step3: Simplify

$\sqrt{6^2}=6$.

Answer:

$6$