Question

question 2 of 5
select the correct answer from each drop - down menu.
using the line segment shown, derive the distance formula.
$d^{2}=(3 - (-5)
)$

Explanation:

Step1: Consider two - point form

Let the two points be $(x_1,y_1)$ and $(x_2,y_2)$. By constructing a right - triangle with the line segment as the hypotenuse, the horizontal distance between the two points is $\vert x_2 - x_1\vert$ and the vertical distance is $\vert y_2 - y_1\vert$.

Step2: Apply Pythagorean theorem

In a right - triangle, if the lengths of the two legs are $a=\vert x_2 - x_1\vert$ and $b = \vert y_2 - y_1\vert$ and the length of the hypotenuse is $d$, then $d^{2}=(x_2 - x_1)^{2}+(y_2 - y_1)^{2}$. So the missing operation in $d^{2}=(3-(-5))^{2}+\text{(vertical distance)}^2$ is $+$.

Answer:

$+$