Question

find the distance between the points (3, 4) and (-1, 0).
a 8
b $2\sqrt{5}$
c 4
d $4\sqrt{2}$

Explanation:

Step1: Identify 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 values

Let $(x_1,y_1)=(3,4)$ and $(x_2,y_2)=(-1,0)$. Then $x_2 - x_1=-1 - 3=-4$ and $y_2 - y_1=0 - 4=-4$.

Step3: Substitute into formula

$d=\sqrt{(-4)^2+(-4)^2}=\sqrt{16 + 16}=\sqrt{32}$.

Step4: Simplify

$\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}$.

Answer:

D. $4\sqrt{2}$