Question

what is the distance between the points (2, 1) and (14, 6) on a coordinate plane?
a. 14 units
b. 5 units
c. 13 units
d. 12 units

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: Substitute values

Here, $x_1 = 2,y_1 = 1,x_2=14,y_2 = 6$. So $d=\sqrt{(14 - 2)^2+(6 - 1)^2}=\sqrt{12^2 + 5^2}$.

Step3: Calculate squares and sum

$12^2=144$, $5^2 = 25$, then $12^2+5^2=144 + 25=169$. So $d=\sqrt{169}$.

Step4: Find square - root

$\sqrt{169}=13$.

Answer:

C. 13 units