Question 1

Given the points $$A = (2, 3)$$ and $$B = (6, 11)$$, what is the distance between them? Use the distance formula.

Accepted Answer

$$d = \sqrt{(6-2)^2$ + (11-3)^2$} = \sqrt{16 + 64} = \sqrt{80} = 4\sqrt{5}$$

Question 2

What is the midpoint of the segment joining $$P_1 = (-4$$, 7)$$ and P_2$ = (2, -1)$$?

Accepted Answer

$$M = \left( \frac{-4+2}{2}, \frac{7+(-1)}{2} \right) = (-1, 3)$$

Question 3

Which quadrant does the point $$(-5, 4)$$ lie in?

Accepted Answer

Quadrant II

Question 4

A hospital is located at $$(1, 2)$$ and a fire station at $$(5, 8). $$What is the straight-line distance between them?

Accepted Answer

$$d = \sqrt{(5-1)^2$ + (8-2)^2$} = \sqrt{16 + 36} = \sqrt{52} = 2\sqrt{13}$$

Question 5

Find the $$x-$$intercepts of the equation $$y = x^2$ - 4.$$

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 6

Which of the following points is on the graph of $$4x - 3y = -24$$?

Accepted Answer

$$( -9, 4 )$$

Question 7

A graph is symmetric with respect to the $$y-$$axis if:

Accepted Answer

Replacing $$x$$ with $$-x$$ yields an equivalent equation.

Question 8

Given the equation $$y = x^2$, which type of symmetry does its graph have?

Accepted Answer

Symmetry with respect to the $$y-$$axis

Question 9

If the midpoint of the segment from $$(a, 2) to$$ $$(6, 8) is$$ $$(4, 5)$$, what is the value of $$a$$?

Accepted Answer

$$a = 2$$

Question 10

Which of the following equations is symmetric with respect to the origin?

Accepted Answer

$$y = x^3$

Question 11

A company wants to build a warehouse exactly halfway between two distribution centers at $$(10, 4)$$ and $$(2, 8). $$What are the coordinates of the warehouse?

Accepted Answer

$$(6, 6)$$

Question 12

Which of the following best describes the $$y-$$intercept of a graph?

Accepted Answer

The point where the graph crosses the $$y-$$axis

Question 13

For the equation $$y = x^2$ - 2x - 3$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 3$$ and $$x = -1$$

Question 14

Which test would you use to check if the graph of $$y = x^4$ is symmetric with respect to the y$-axis?

Accepted Answer

Replace $$x$$ with $$-x$$ and check if the equation is unchanged.

Question 15

A graph touches but does not cross the $$x-$$axis at $$(2, 0). $$What does this mean about the equation's roots?

Accepted Answer

There is a repeated root at $$x = 2.$$

Question 16

Which of the following is the correct procedure to find the $$x-$$intercept(s) of a graph?

Accepted Answer

Let $$y = 0$$ and solve for $$x.$$

Question 17

If a graph is symmetric with respect to the $$x-$$axis, which of the following must be true?

Accepted Answer

For every $$(x, y) on $$the graph, $$(x, -y) is $$also on the graph.

Question 18

Which of the following equations is NOT symmetric with respect to the $$y-$$axis?

Accepted Answer

$$y = x^3$

Question 19

A city park is located at $$(0, 0). If a $$playground is at $$(6, 8)$$, what is the distance from the park to the playground?

Accepted Answer

$$d = \sqrt{(6-0)^2$ + (8-0)^2$} = \sqrt{36 + 64} = \sqrt{100} = 10$$

Distance and Midpoint Formulas; Graphs, Intercepts, and Symmetry in the Coordinate Plane

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