Question

find the distance between the points (4, 10) and (0, 1). write your answer as a whole number or a fully simplified radical expression. do not round.

Explanation:

Step1: Identify the distance formula

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

Step2: Assign the values

Let $(x_1,y_1)=(4,10)$ and $(x_2,y_2)=(0,1)$. Then $x_2 - x_1=0 - 4=-4$ and $y_2 - y_1=1 - 10=-9$.

Step3: Calculate the squares

$(x_2 - x_1)^2=(-4)^2 = 16$ and $(y_2 - y_1)^2=(-9)^2 = 81$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=16 + 81=97$.

Step5: Find the distance

$d=\sqrt{97}$

Answer:

$\sqrt{97}$