Question

1. what is the distance between (0, 0) and (3, 4)?

a. 3
b. 4
c. 7
d. 5

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, $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(3,4)$.

Step2: Substitute values

Substitute $x_1 = 0,y_1 = 0,x_2 = 3,y_2 = 4$ into the formula: $d=\sqrt{(3 - 0)^2+(4 - 0)^2}=\sqrt{3^2+4^2}$.

Step3: Calculate squares and sum

$3^2=9$, $4^2 = 16$, so $d=\sqrt{9 + 16}=\sqrt{25}$.

Step4: Find square - root

$\sqrt{25}=5$.

Answer:

d. 5