Question

what is the distance between (0, 0) and (3, 4)?
a. 7
b. 4
c. 5
d. 3

Explanation:

Step1: Recall distance formula

For points $(x_1,y_1)$ and $(x_2,y_2)$, distance $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Substitute given points

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

Step3: Calculate squared terms

$d=\sqrt{3^2+4^2}=\sqrt{9+16}$

Step4: Simplify the expression

$d=\sqrt{25}=5$

Answer:

c. 5