Question 1

Which of the following best describes the difference between a global (spherical) coordinate system and a projected coordinate system as used in Geographic Information Systems (GIS)?

Accepted Answer

A global coordinate system uses latitude and longitude to define locations on a sphere, while a projected coordinate system translates these locations onto a two-dimensional Cartesian plane.

Question 2

Given the points $$A(-2, -1)$$ and $$B(6, 7)$$, what is the distance between them? Provide your answer in simplified radical form.

Accepted Answer

Question 3

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

Accepted Answer

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

Question 4

A circle has its center at $$(0, -6)$$ and a radius of $$10. $$What is the standard form of its equation?

Accepted Answer

$$(x - 0)^2$ + (y + 6)^2$ = 100$$

Question 5

Which of the following ordered pairs is a solution to the equation $$y = 2x + 3$$?

Accepted Answer

$$(1, 5)$$

Question 6

What is the $$x-$$intercept of the line given by the equation $$3x - 6y = 12$$?

Accepted Answer

$$(4, 0)$$

Question 7

Which of the following best describes the radius of a circle?

Accepted Answer

The distance from the center to any point on the circle.

Question 8

Given the endpoints of a diameter of a circle at $$(-2, 3)$$ and $$(-1, 1)$$, what is the equation of the circle in standard form?

Accepted Answer

$$(x + 1.5)^2$ + (y - 2)^2$ = 2.5$$

Question 9

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

Accepted Answer

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

Question 10

A city uses a projected coordinate system to map its streets. If the city is represented on a Cartesian plane, which of the following best describes the axes?

Accepted Answer

The $$x-$$axis is the horizontal number line and the $$y-$$axis is the vertical number line.

Question 11

If a linear equation is given as $$y = mx + b$$, what does the parameter $$b$$ represent?

Accepted Answer

The $$y-$$intercept of the line.

Question 12

Which of the following best describes the process of graphing a linear equation using an $$x$$-$$y$$ table?

Accepted Answer

Choose several values for $$x$$, compute the corresponding $$y$$ values, plot the points, and connect them with a straight line.

Question 13

A GPS device uses which type of coordinate system to determine your location on Earth?

Accepted Answer

Global (spherical) coordinate system

Question 14

If the equation of a line is $$y = -\frac{1}{2}x + 4$$, what is the slope of the line?

Accepted Answer

$$-\frac{1}{2}$$

Question 15

Which of the following real-world applications would most likely use a projected coordinate system?

Accepted Answer

Mapping city streets for urban planning

Question 16

If a line passes through the points $$(2, 3)$$ and $$(4, 7)$$, what is the slope of the line?

Accepted Answer

$$2$$

Question 17

Which of the following statements is true about the $$y-$$intercept of a function?

Accepted Answer

It is the point where the graph crosses the $$y-$$axis.

Question 18

A hospital uses a rectangular coordinate system to track patient rooms on each floor. If room A is at $$(3, 5)$$ and room B is at $$(7, 8)$$, what is the midpoint between these two rooms?

Accepted Answer

$$(5, 6.5)$$

Question 19

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

Accepted Answer

A diagonal number line

Question 20

If the equation of a circle is $$(x - 2)^2$ + (y + 3)^2$ = 25$$, what are the coordinates of the center and the radius?

Accepted Answer

Center: $$(2, -3)$$, Radius: $$5$$

Chapter 1: Graphs, Functions, and Models – Foundations of Graphing in College Algebra

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