Question

what is the distance between the points (1, 2) and (4, 6)?
○ 5
○ 3
○ 4
○ 7

Explanation:

Step1: Recall distance formula

The distance $d$ 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: Substitute given points

Let $(x_1,y_1)=(1,2)$ and $(x_2,y_2)=(4,6)$. Substitute values:
$d=\sqrt{(4-1)^2+(6-2)^2}$

Step3: Calculate differences

Compute the squared differences:
$d=\sqrt{(3)^2+(4)^2}$

Step4: Simplify the expression

Calculate squares and sum, then take root:
$d=\sqrt{9+16}=\sqrt{25}=5$

Answer:

A. 5