Question 1

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

Accepted Answer

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

Question 2

Given the points $$P(2, 5)$$ and $$Q(8, -3)$$, what is the midpoint of the line segment $$\overline{PQ}$$?

Accepted Answer

$$(5, 1)$$

Question 3

A city park is located at $$(3, 7)$$ and a hospital is at $$(11, 15). $$What is the straight-line distance between them?

Accepted Answer

$$\sqrt{128}$$

Question 4

Which of the following is the correct formula for the midpoint $$M of a $$segment with endpoints $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$)$$?

Accepted Answer

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

Question 5

If the equation $$y = 2x + 3 is $$graphed in the rectangular coordinate system, what is the y-intercept?

Accepted Answer

$$(0, 3)$$

Question 6

A delivery drone starts at $$(1, 2)$$ and must reach $$(7, 10). $$What is the minimum distance it must travel?

Accepted Answer

$$\sqrt{36 + 64}$$

Question 7

Which of the following points lies on the graph of the equation $$y = x^2$ - 4x + 3$$?

Accepted Answer

$$(2, -1)$$

Question 8

A line segment has endpoints $$A(-2, 4)$$ and $$B(6, -8). $$What is the midpoint of $$\overline{AB}$$?

Accepted Answer

$$(2, -2)$$

Question 9

If the distance between two points is $$10$$ and their coordinates are $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$, which equation must be true?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$} = 10$$

Question 10

A biologist tracks two tagged animals at $$(5, 12)$$ and $$(13, 20). $$What is the midpoint of their locations?

Accepted Answer

$$(9, 16)$$

Question 11

Which of the following equations represents a vertical line in the rectangular coordinate system?

Accepted Answer

$$x = 4$$

Question 12

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

$$10$$

Question 13

Which of the following is NOT a property of the rectangular coordinate system?

Accepted Answer

The axes are parallel to each other

Question 14

If the equation $$y = -3x + 7$$ models the cost $$y (in $$dollars) of producing $$x$$ units, what is the cost when $$x = 2$$?

Accepted Answer

$$1$$

Question 15

A segment has endpoints $$(a, b)$$ and $$(c, d). $$Which formula gives the midpoint?

Accepted Answer

$$\left( \frac{a + c}{2}, \frac{b + d}{2} \right)$$

Question 16

Which of the following points is NOT on the graph of $$y = 2x - 5$$?

Accepted Answer

$$(1, 0)$$

Question 17

A chemist plots the temperature of a reaction over time. If the temperature at $$t = 0 is$$ $$20^\circC $$and increases by $$5^\circC $$per minute, which equation models this?

Accepted Answer

$$y = 5x + 20$$

Question 18

A segment has endpoints $$(7, -2)$$ and $$(1, 4). $$What is the distance between them?

Accepted Answer

$$\sqrt{(7 - 1)^2$ + (-2 - 4)^2$}$$

Question 19

Which of the following equations represents a horizontal line?

Accepted Answer

$$y = -3$$

Question 20

A medical researcher records the position of a cell at $$(2, 3)$$ and $$(10, 11). $$What is the midpoint of the cell's movement?

Accepted Answer

$$(6, 7)$$

Fundamental Concepts in the Rectangular Coordinate System

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