Question 1

Which of the following ordered pairs is plotted correctly on the Cartesian coordinate system?

Accepted Answer

The point (3, 7) is located 3 units right and 7 units up from the origin.

Question 2

A medium pizza with three toppings costs $11. Which of the following ordered pairs best represents this scenario?

Accepted Answer

$$(3, 11)$$

Question 3

Given the right triangle shown, which equation correctly represents the Pythagorean Theorem?

Accepted Answer

$$a^2$$ + $$b^2$$ = $$c^2$$

Question 4

A 50-inch TV has a height of 24.5 inches. Using the Pythagorean Theorem, what is the width of the TV (to the nearest tenth)?

Accepted Answer

$$\sqrt{50^2$ - 24.5^2$} \approx 44.6$$ inches

Question 5

Which formula is used to calculate the distance between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$) in $$the plane?

Accepted Answer

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

Question 6

Calculate the distance between the points $$(-1, 1)$$ and $$(-6, 5)$$ using the distance formula. Round to the nearest whole number.

Accepted Answer

$$\sqrt{(-6 + 1)^2$ + (5 - 1)^2$} = \sqrt{25 + 16} = \sqrt{41} \approx 6$$

Question 7

Which formula is used to find the midpoint between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Question 8

The median age at first marriage for women increased from 20.8 in 1970 to 26.1 in 2012. What is the midpoint of these data points $$(20.8, 1970)$$ and $$(26.1, 2012)$$?

Accepted Answer

$$(23.45, 1991)$$

Question 9

Which of the following best describes the x-axis in the Cartesian coordinate system?

Accepted Answer

It is the horizontal axis where $$y = 0.$$

Question 10

A baby’s back is measured from the shoulder at $$(-1, 1) to $$the bottom at $$(-6, 5). $$What is the length of the back, rounded to the nearest whole number?

Accepted Answer

$$6$$

Question 11

Which of the following is a correct application of the Pythagorean Theorem in a real-world context?

Accepted Answer

Calculating the diagonal length of a rectangular TV given its width and height.

Question 12

If the endpoints of a line segment are $$(4, 7)$$ and $$(10, 15)$$, what is the midpoint?

Accepted Answer

$$(7, 11)$$

Question 13

Which of the following is NOT a correct use of the distance formula?

Accepted Answer

Finding the midpoint between two points.

Question 14

If a right triangle has legs of length 9 and 12, what is the length of the hypotenuse?

Accepted Answer

$$\sqrt{9^2$ + 12^2$} = \sqrt{81 + 144} = \sqrt{225} = 15$$

Question 15

Which of the following points lies in Quadrant II of the Cartesian coordinate system?

Accepted Answer

$$(-4, 2)$$

Equations, Inequalities, and Modeling: The Cartesian Coordinate System, Pythagorean Theorem, Distance and Midpoint Formulas

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