Question

1. determine the distance between points e(-3, 6) and f(3, 2).

2√13 units
13√2 units
2√6 units
7 units

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-3,y_1 = 6,x_2=3,y_2 = 2$.

Step2: Substitute values

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

Step3: Calculate squares and sum

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

Step4: Simplify square - root

$\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}$.

Answer:

$2\sqrt{13}$ units