Question 1

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

Accepted Answer

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

Question 2

Given the points $$P(2, -3)$$ and $$Q(-4, 5)$$, what is the distance between them?

Accepted Answer

$$d = \sqrt{(2 - (-4))^2$ + (-3 - 5)^2$} = \sqrt{36 + 64} = 10$$

Question 3

What are the coordinates of the midpoint $$M of $$the segment joining $$A(-6, 8)$$ and $$B(4, -2)$$?

Accepted Answer

$$M = (\frac{-6 + 4}{2}, \frac{8 + (-2)}{2}) = (-1, 3)$$

Question 4

A city wants to build a park exactly halfway between two schools located at $$(3, 7)$$ and $$(11, -1). $$What are the coordinates for the park?

Accepted Answer

$$(7, 3)$$

Question 5

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

Accepted Answer

Quadrant II

Question 6

If the endpoints of a diameter of a circle are $$A(1, -2)$$ and $$B(-1, 2)$$, what is the radius of the circle?

Accepted Answer

$$r = \frac{\sqrt{(1 - (-1))^2$ + ((-2) - 2)^2$}}{2} = \frac{\sqrt{4 + 16}}{2} = \frac{\sqrt{20}}{2} = \sqrt{5}$$

Question 7

Which of the following points lies on the y-axis?

Accepted Answer

$$(0, 7)$$

Question 8

Given triangle $$ABC$$ with $$A(-2, 1)$$, $$B(2, 3)$$, and $$C(3, 1)$$, which side is the longest?

Accepted Answer

$$BC$$

Question 9

A drone flies from $$(1, 3) to$$ $$(5, 6). $$What is the straight-line distance it travels?

Accepted Answer

$$d = \sqrt{(5 - 1)^2$ + (6 - 3)^2$} = \sqrt{16 + 9} = 5$$

Question 10

Which of the following best describes the Cartesian coordinate system?

Accepted Answer

A plane defined by two perpendicular axes, the x-axis and y-axis, intersecting at the origin

Question 11

If a point is located at $$(x, y)$$ where $$x \u003e 0$$ and $$y \u003c 0$$, in which quadrant does it lie?

Accepted Answer

Quadrant IV

Question 12

A cell phone tower is at $$(0, 0)$$ and a user is at $$(8, 15). $$What is the distance between them?

Accepted Answer

$$d = \sqrt{8^2$ + 15^2$} = \sqrt{64 + 225} = \sqrt{289} = 17$$

Question 13

Which formula gives the midpoint $$M of $$the segment joining $$P_1$$($$x_1$$, $$y_1$$)$$ and P_2$(x_2$, y_2$)$$?

Accepted Answer

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

Question 14

A triangle has vertices at $$A(0, 0)$$, $$B(4, 0)$$, and $$C(0, 3). $$What is the area of the triangle?

Accepted Answer

$$6$$

Question 15

Which of the following points is in Quadrant III?

Accepted Answer

$$(-2, -5)$$

Question 16

If the midpoint of a segment is $$(2, -1)$$ and one endpoint is $$(4, 3)$$, what is the other endpoint?

Accepted Answer

$$(0, -5)$$

Question 17

A rectangular field has corners at $$(1, 1)$$, $$(1, 6)$$, $$(8, 1)$$, and $$(8, 6). $$What is the length of the diagonal?

Accepted Answer

$$d = \sqrt{(8 - 1)^2$ + (6 - 1)^2$} = \sqrt{49 + 25} = \sqrt{74}$$

Question 18

Which of the following is NOT a property of the Cartesian coordinate system?

Accepted Answer

The axes are parallel to each other

Graphs: The Distance and Midpoint Formulas in the Coordinate Plane

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