Question

18 find, in simplest radical form, the length of the line segment with endpoints whose coordinates are (-1,4) and (3,-2).

Explanation:

Step1: Recall distance formula

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

Step2: Identify coordinates

Here $x_1=-1,y_1 = 4,x_2=3,y_2=-2$.

Step3: Substitute values

$d=\sqrt{(3-(-1))^2+((-2 - 4))^2}=\sqrt{(3 + 1)^2+(-6)^2}=\sqrt{4^2+(-6)^2}$.

Step4: Calculate squares

$\sqrt{16 + 36}=\sqrt{52}$.

Step5: Simplify radical

$\sqrt{4\times13}=2\sqrt{13}$.

Answer:

$2\sqrt{13}$