Question

question
find the distance between the two points in simplest radical form.
(6, -4) and (1, -6)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Let $(x_1,y_1)=(6,-4)$ and $(x_2,y_2)=(1,-6)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$.
$x_2 - x_1=1 - 6=-5$.
$y_2 - y_1=-6-(-4)=-6 + 4=-2$.

Step3: Square the differences

$(x_2 - x_1)^2=(-5)^2 = 25$.
$(y_2 - y_1)^2=(-2)^2 = 4$.

Step4: Sum and take square - root

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{25 + 4}=\sqrt{29}$.

Answer:

$\sqrt{29}$