Question

question 3 of 10
what is the distance between the points (2, 1) and (14, 6) on a coordinate plane?

a. 12 units
b. 14 units
c. 5 units
d. 13 units

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: Identify coordinates

Here, \(x_1 = 2\), \(y_1 = 1\), \(x_2 = 14\), \(y_2 = 6\).

Step3: Substitute into formula

Calculate \(x_2 - x_1 = 14 - 2 = 12\) and \(y_2 - y_1 = 6 - 1 = 5\).
Then, \(d=\sqrt{(12)^2+(5)^2}=\sqrt{144 + 25}=\sqrt{169}\).

Step4: Simplify the square root

\(\sqrt{169}=13\).

Answer:

D. 13 units