Question

find the distance between the pair of points. if necessary, express answers in simplified radical form and then round to two decimal places. (7,3) and (1,11) the distance between the points is units. (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, $x_1 = 7,y_1 = 3,x_2=1,y_2 = 11$.

Step2: Calculate differences

$x_2 - x_1=1 - 7=-6$ and $y_2 - y_1=11 - 3 = 8$.

Step3: Square the differences

$(x_2 - x_1)^2=(-6)^2 = 36$ and $(y_2 - y_1)^2=8^2 = 64$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 64=100$.

Step5: Take the square - root

$d=\sqrt{100}=10$.

Answer:

10