Question

find the distance between the points (1, 3) and (-2, -9). write your answer as a whole number or a fully simplified radical expression. do not round. units

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: Substitute the given points

Let $(x_1,y_1)=(1,3)$ and $(x_2,y_2)=(-2,-9)$. Then $x_2 - x_1=-2 - 1=-3$ and $y_2 - y_1=-9 - 3=-12$.

Step3: Calculate the squares and sum

$(x_2 - x_1)^2=(-3)^2 = 9$ and $(y_2 - y_1)^2=(-12)^2 = 144$. The sum is $9 + 144=153$.

Step4: Simplify the radical

$d=\sqrt{153}=\sqrt{9\times17}=3\sqrt{17}$.

Answer:

$3\sqrt{17}$