Question

find the distance between the pair of points. if necessary, express answers in simplified radical form and then round to two decimal places.
(1,2) and (7,10)
the distance between the points is (square) units.
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify the 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, $x_1 = 1,y_1 = 2,x_2 = 7,y_2 = 10$.

Step2: Substitute the values into the formula

$d=\sqrt{(7 - 1)^2+(10 - 2)^2}=\sqrt{6^2+8^2}$.

Step3: Calculate the squares

$\sqrt{6^2+8^2}=\sqrt{36 + 64}$.

Step4: Add the numbers inside the square - root

$\sqrt{36 + 64}=\sqrt{100}$.

Step5: Simplify the square - root

$\sqrt{100}=10$.

Answer:

$10$