Question

Question 1: Find the distance between the points (1, 4) and (5, 1).

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(5-1)^2+(1-4)^2}\implies d=\sqrt{4^2+(-3)^2} \\\\\\ d=\sqrt{16+9}\implies d=\sqrt{25}\implies d=5$

Answer 2

Answer: second option.

Step-by-step explanation:

You need to use the formula for calculate the distance between two points. This is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Given the point (1, 4) and the point (5, 1), you can say that:

$x_2=5\\x_1=1\\y_2=1\\y_1=4$

Now you must substitute these values into the formula.

The distance between the points (1, 4) and (5, 1) is the following:

$d=\sqrt{(5-1)^2+(1-4)^2}\\\\d=5$

This matches with the second option.