Q: Which of the following is the correct set notation for the months January, April, and May?

$$\{\text{January}, \text{April}, \text{May}\}$$

Question 1

Which formula correctly represents the distance $$d$$ between two points $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$) in $$the coordinate plane?

Accepted Answer

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

Question 2

Given the points $$A(-3, -5)$$ and $$B(3, 3)$$, what is the distance between them?

Accepted Answer

$$10$$

Question 3

What is the midpoint of the segment joining the points $$(-6, -6)$$ and $$(-5, -2)$$?

Accepted Answer

$$\left( -5.5, -4 \right)$$

Question 4

Which of the following best describes the coordinates of a point in Quadrant II?

Accepted Answer

$$x  0$$

Question 5

Kenya drives 3 miles west and Pete drives 8 miles north from the same starting point. How far apart are they, to the nearest hundredth?

Accepted Answer

$$8.54$$ miles

Question 6

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

Accepted Answer

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

Question 7

If $$C is $$the midpoint of $$\overline{AB}$$, $$A = (2, 5)$$, and $$B = (6, 9)$$, what are the coordinates of $$C$$?

Accepted Answer

$$\left( 4, 7 \right)$$

Question 8

Which set notation correctly lists all multiples of 3 between 0 and 21, inclusive?

Accepted Answer

$$\{0, 3, 6, 9, 12, 15, 18, 21\}$$

Question 9

Which interval notation represents all real numbers $$x$$ such that $$2 \u003c x \leq 7$$?

Accepted Answer

$$(2, 7]$$

Question 10

A company requires employees to work at least 60 hours but no more than 120 hours in a summer program. Which interval notation represents the possible number of hours an employee can work?

Accepted Answer

$$[60, 120]$$

Question 11

If the distance between points $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$) is$$ $$0$$, what can you conclude about $$A$$ and $$B$$?

Accepted Answer

$$A$$ and $$B$$ are the same point.

Question 12

Which of the following is the correct set notation for the months January, April, and May?

Accepted Answer

$$\{	ext{January}, 	ext{April}, 	ext{May}\}$$

Question 13

Which of the following points is NOT in Quadrant IV?

Accepted Answer

$$(-2, -3)$$

Question 14

If $$A = (1, 2)$$ and $$B = (7, 8)$$, what is the length of $$\overline{AB}$$?

Accepted Answer

$$6\sqrt{2}$$

Question 15

Which of the following is the correct interval notation for all real numbers $$x$$ such that $$x \u003e 5$$?

Accepted Answer

$$(5, \infty)$$

Question 16

If $$M is $$the midpoint of $$\overline{AB}$$, $$A = (a, b)$$, $$B = (c, d)$$, and $$M = (5, 7)$$, $$A = (3, 4)$$, what are the coordinates of $$B$$?

Accepted Answer

$$(7, 10)$$

Question 17

Which of the following best describes the abscissa of a point $$(x, y)$$?

Accepted Answer

The $$x-$$coordinate

Question 18

Which of the following is the correct set notation for all $$x$$ such that $$x is an $$integer and $$1 \leq x \u003c 5$$?

Accepted Answer

$$\{1, 2, 3, 4\}$$

Question 19

If $$A = (x_1$, y_1$)$$ and $$B = (x_2$, y_2$)$$, which expression represents the change in $$x-$$coordinates from $$A to$$ $$B$$?

Accepted Answer

$$x_2$$ - $$x_1$$

Distance and Midpoint Formulas in the Cartesian Plane

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