Question

find the distance between the pair of points. if necessary, express answers in simplified radical form and then round to two decimal places. (10,3) and (1,15) the distance between the points is units. (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Substitute the given points

Let $(x_1,y_1)=(10,3)$ and $(x_2,y_2)=(1,15)$. Then $d=\sqrt{(1 - 10)^2+(15 - 3)^2}$.

Step3: Calculate the differences

First, $1-10=-9$ and $15 - 3 = 12$. So $d=\sqrt{(-9)^2+12^2}$.

Step4: Calculate the squares

$(-9)^2 = 81$ and $12^2=144$. Then $d=\sqrt{81 + 144}$.

Step5: Calculate the sum

$81+144 = 225$. So $d=\sqrt{225}$.

Step6: Simplify the radical

$\sqrt{225}=15$.

Answer:

$15$