Question

question 2 of 5 select the correct answer from each drop - down menu. using the line segment shown, derive the distance formula. d² = √ 3 - (-3) -2 - (-5) 3 - (-5) 3 + (-5) ² ( )² submit

Explanation:

Step1: Recall distance formula concept

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ in a coordinate - plane is based on the Pythagorean theorem. If we consider a right - triangle formed by the two points, the horizontal side length is $|x_2 - x_1|$ and the vertical side length is $|y_2 - y_1|$. Then $d^{2}=(x_2 - x_1)^{2}+(y_2 - y_1)^{2}$.
Let's assume the two points are $(x_1,y_1)$ and $(x_2,y_2)$. We need to find the differences in the $x$ and $y$ coordinates.

Step2: Identify coordinates from the problem context

Without seeing the actual coordinates of the two points on the line - segment from the graph (assuming the points are $(x_1,y_1)$ and $(x_2,y_2)$), if we assume the correct difference in $x$ - coordinates is the first part of the right - hand side of $d^{2}$ and the correct difference in $y$ - coordinates is the second part. If we assume the two points have $x$ - coordinates such that the difference is calculated as one of the given expressions.
Let's assume the two points have $x$ - coordinates that give a difference of $3-(- 5)$. Then the distance formula for the squared distance $d^{2}=(3 - (-5))^{2}+(y_2 - y_1)^{2}$.

Answer:

The first blank should be filled with $3-(-5)$ and the second and third blanks should be filled with appropriate $y$ - coordinate differences (not given in the options completely in the current problem statement, but conceptually it would be of the form $(y_2 - y_1)^{2}$). If we only consider the $x$ - coordinate part for the given options, the answer for the first drop - down is $3-(-5)$.