Question 1

Which of the following ordered pairs represents the relationship between the category 'housing' and the amount spent on it, given the data (housing, $19,884)?

Accepted Answer

$$(	ext{housing},\ 19884)$$

Question 2

Given points $$P(-4, 3)$$ and $$R(8, -2)$$, what is the distance between them using the distance formula?

Accepted Answer

$$\sqrt{(8 - (-4))^2$ + (-2 - 3)^2$} = \sqrt{12^2$ + (-5)^2$} = \sqrt{144 + 25} = \sqrt{169} = 13$$

Question 3

Which formula correctly 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 4

If the midpoint of a segment is $$(8, -2)$$ and one endpoint is $$(-6, 12)$$, what are the coordinates of the other endpoint?

Accepted Answer

$$(22, -16)$$

Question 5

Given the points $$M(-2, 5)$$, $$N(12, 3)$$, and $$Q(10, -11)$$, are these the vertices of a right triangle?

Accepted Answer

Yes, because the square of the length of the longest side equals the sum of the squares of the other two sides.

Question 6

Three points $$A$$, $$B$$, and $$C$$ are collinear if:

Accepted Answer

The sum of the distances between two pairs of points equals the distance between the remaining pair.

Question 7

Estimate the sales from fast-food restaurants in 2014 using the midpoint formula, given sales were $$167.7$$ billion in 2011 and $$233.7$$ billion in 2017.

Accepted Answer

$$200.7$$ billion

Question 8

Which equation represents the graph of a parabola?

Accepted Answer

$$y = x^2$ - 4$$

Question 9

If $$y = 4x - 1$$, which of the following is an ordered pair solution?

Accepted Answer

$$(1, 3)$$

Question 10

Which of the following steps is NOT part of graphing an equation by point plotting?

Accepted Answer

Find the slope of the line using two points.

Question 11

Given the equation $$x = \sqrt{y - 1}$$, which of the following is a solution?

Accepted Answer

$$(1, 2)$$

Question 12

Which quadrant does the point $$(-3, 4)$$ lie in?

Accepted Answer

Quadrant II

Question 13

If the equation is $$y = x^2$ - 4$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, -4)$$

Question 14

Which of the following is the correct distance formula for points $$P(x_1$, y_1$)$$ and $$Q(x_2$, y_2$)$$?

Accepted Answer

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

Question 15

A real-world application: A drone flies from $$(2, 3) to$$ $$(10, 15). $$What is the straight-line distance it travels?

Accepted Answer

$$\sqrt{(10 - 2)^2$ + (15 - 3)^2$} = \sqrt{8^2$ + 12^2$} = \sqrt{64 + 144} = \sqrt{208} \approx 14.42$$

Question 16

If a segment has endpoints $$(a, b)$$ and $$(c, d)$$, and its midpoint is $$(m, n)$$, which equation must be true?

Accepted Answer

$$m = \frac{a + c}{2}$$ and $$n = \frac{b + d}{2}$$

Graphs and Functions: Rectangular Coordinates, Distance, and Midpoint Formulas

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