Question

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

Question 1 options:

7

5

25

√7

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 = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=√((5-1)^2+(1-4)^2)\implies d=√(4^2+(-3)^2) \\\\\\ d=√(16+9)\implies d=√(25)\implies d=5`

Answer 2

Answer: second option.

Explanation:

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

`d=√((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=√((5-1)^2+(1-4)^2)\\\\d=5`

This matches with the second option.