Question 1

Which formula is used to find the distance between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$) in $$the rectangular coordinate system?

Accepted Answer

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

Question 2

Given the points $$A(2, 3)$$ and $$B(8, 7)$$, what is the midpoint of the line segment connecting them?

Accepted Answer

$$(5, 5)$$

Question 3

A biologist tracks the movement of a tagged animal from $$(1, 2) to$$ $$(4, 6). $$What is the straight-line distance the animal traveled?

Accepted Answer

$$\sqrt{9 + 16}$$

Question 4

Which of the following is the correct equation for the graph of a line passing through $$(0, 0)$$ and $$(2, 4)$$?

Accepted Answer

$$y = 2x$$

Question 5

A city planner wants to find the midpoint between two locations at $$(3, 8)$$ and $$(9, 2). $$What is the midpoint?

Accepted Answer

$$(6, 5)$$

Question 6

If the distance between $$(x_1$, y_1$)$$ and $$(x_2$, y_2$) is$$ $$10$$, and $$x_1 = 1$, y_1$ = 2$$, $$x_2 = 7$, what is y_2$?

Accepted Answer

$$y_2 = 8$

Question 7

Which of the following points lies on the line $$y = 3x - 2$$?

Accepted Answer

$$(1, 1)$$

Question 8

A runner starts at $$(0, 0)$$ and finishes at $$(6, 8). $$What is the total distance covered if the runner moves in a straight line?

Accepted Answer

$$\sqrt{36 + 64}$$

Question 9

Which formula gives the midpoint $$M of a $$segment with endpoints $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$M = \left( \frac{x_1$ + x_2$}{2}, \frac{y_1$ + y_2$}{2} \right)$$

Question 10

A chemist plots the temperature change over time and gets the equation $$y = 5x + 3. $$What is the $$y-$$intercept of this graph?

Accepted Answer

$$3$$

Question 11

If the endpoints of a segment are $$(-2, 4)$$ and $$(6, -8)$$, what is the distance between them?

Accepted Answer

$$\sqrt{(6 - (-2))^2$ + (-8 - 4)^2$}$$

Question 12

A medical researcher records patient data at $$(5, 12)$$ and $$(13, 4). $$What is the midpoint of these two data points?

Accepted Answer

$$(9, 8)$$

Question 13

Which of the following equations represents a line with slope $$-2$$ and $$y-$$intercept $$5$$?

Accepted Answer

$$y = -2x + 5$$

Question 14

A surveyor measures two points: $$(7, 3)$$ and $$(2, 11). $$What is the distance between them?

Accepted Answer

$$\sqrt{(7 - 2)^2$ + (3 - 11)^2$}$$

Question 15

Which of the following is NOT a correct way to graph an equation in the rectangular coordinate system?

Accepted Answer

Ignoring the relationship between $$x$$ and $$y$$

Fundamental Concepts in the Rectangular Coordinate System

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