Question 1

Which of the following points lies in Quadrant II of the Cartesian plane?

Accepted Answer

A point with coordinates $$(-6, 4)$$

Question 2

Given the points $$P(1, 2)$$ and $$Q(-3, 5)$$, what is the distance $$d$$ between them?

Accepted Answer

$$d = 5$$

Question 3

What is the formula for the midpoint $$M$$ between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Question 4

Find the intersection $$(A \cap B)$$, where $$A = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, \ldots\}$$ and $$B = \{1, 3, 5, 7, 9, 11, \ldots\}.$$

Accepted Answer

$$\{1, 3, 5, 7, 9, 11, \ldots\}$$

Question 5

Which of the following intervals represents the union $$( -1, 1 ) \cup [0, 6 ]$$?

Accepted Answer

$$(-1, 6]$$

Question 6

A city is planning to build a park that is exactly halfway between two schools located at $$(3, -10)$$ and $$(-1, 2). $$What are the coordinates of the park?

Accepted Answer

$$(1, -4)$$

Question 7

Given the sets $$C = \{0, 2, 4, 6, 8, 10, \ldots\}$$ and $$D = \{2, 3, 5, 7, 11, 13, \ldots\}$$, what is $$C \cap D$$?

Accepted Answer

$$\{2\}$$

Question 8

Which of the following best describes the union of the intervals $$(-\infty, 0) \cup [1, 5]$$?

Accepted Answer

$$(-\infty, 0) \cup [1, 5]$$

Question 9

A biologist is tracking two tagged animals. One is at $$(\sqrt{2}, \sqrt{3})$$ and the other at $$(-\sqrt{8}, -\sqrt{12}). $$What is the distance between them?

Accepted Answer

$$3\sqrt{5}$$

Question 10

Which of the following is the correct interval for the intersection $$( -\infty, 4 ] \cap (0, \infty )$$?

Accepted Answer

$$(0, 4]$$

Question 11

If $$A = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, \ldots\}$$ and $$C = \{0, 2, 4, 6, 8, 10, \ldots\}$$, what is $$A \cap C$$?

Accepted Answer

$$\{0, 2, 4, 6, 8, 10, \ldots\}$$

Question 12

A delivery drone must travel from $$(3, -10) to$$ $$(-1, 2). $$What is the straight-line distance it must fly?

Accepted Answer

$$4\sqrt{10}$$

Question 13

Which of the following is the correct result for $$( -\infty, 5 ] \cap [5, 8 )$$?

Accepted Answer

$$\{5\}$$

Question 14

Given $$B = \{1, 3, 5, 7, 9, 11, \ldots\}$$ and $$C = \{0, 2, 4, 6, 8, 10, \ldots\}$$, what is $$B \cup C$$?

Accepted Answer

$$\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, \ldots\}$$

Question 15

A company wants to place a new office exactly halfway between two existing offices at $$(\sqrt{2}, \sqrt{3})$$ and $$(-\sqrt{8}, -\sqrt{12}). $$What are the coordinates of the new office?

Accepted Answer

$$\left( -\frac{\sqrt{2}}{2}, -\frac{\sqrt{3}}{2} \right)$$

Question 16

Which of the following intervals is the intersection of $$(-\infty, 0)$$ and $$[1, 5]$$?

Accepted Answer

Empty set

Question 17

If $$A = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, \ldots\}$$ and $$B = \{1, 3, 5, 7, 9, 11, \ldots\}$$, what is $$A \cup B$$?

Accepted Answer

$$\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, \ldots\}$$

Question 18

A GPS device records two locations: $$\left( \frac{1}{2}, 4 \right)$$ and $$\left( \frac{3}{2}, -1 \right). $$What is the distance between these two points?

Accepted Answer

$$\sqrt{26}$$

Question 19

Given $$C = \{0, 2, 4, 6, 8, 10, \ldots\}$$ and $$D = \{2, 3, 5, 7, 11, 13, \ldots\}$$, what is $$C \cup D$$?

Accepted Answer

$$\{0, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, \ldots\}$$

College Algebra Study Guide: Coordinate Geometry and Set Theory

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