Question 1

Which of the following best describes the coordinates of a point in the Cartesian plane?

Accepted Answer

A pair of real numbers $$(x, y)$$ that uniquely locate a point in the plane.

Question 2

Given the points $$A(2, 3)$$ and $$B(6, 7)$$, what is the distance between them?

Accepted Answer

$$\sqrt{(6-2)^2$ + (7-3)^2$}$$

Question 3

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

Accepted Answer

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

Question 4

A city park is represented on a map with the southwest corner at $$(1, 2)$$ and the northeast corner at $$(7, 8). $$What are the coordinates of the center of the park?

Accepted Answer

$$(4, 5)$$

Question 5

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

Accepted Answer

Quadrant II

Question 6

If the distance between two points is $$10$$ and their $$x-$$coordinates are $$2$$ and $$8$$, what is the difference between their $$y-$$coordinates?

Accepted Answer

$$\pm 8$$

Question 7

A triangle has vertices at $$A(0, 0)$$, $$B(6, 0)$$, and $$C(0, 8). $$What is the length of the hypotenuse $$BC$$?

Accepted Answer

$$10$$

Question 8

Which of the following statements is true about the converse of the Pythagorean Theorem in the context of the distance formula?

Accepted Answer

If the sum of the squares of two sides equals the square of the third side, the triangle is a right triangle.

Question 9

A drone flies from point $$A(1, 2) to $$point $$B(4, 6). $$What is the straight-line distance it travels?

Accepted Answer

$$5$$

Question 10

Given points $$P(-2, 5)$$ and $$Q(4, -1)$$, what are the coordinates of the midpoint of $$PQ$$?

Accepted Answer

$$(1, 2)$$

Question 11

A rectangular garden has opposite corners at $$(2, 3)$$ and $$(8, 9). $$What is the length of the diagonal of the garden?

Accepted Answer

$$6\sqrt{2}$$

Question 12

Which of the following best describes the ordinate of a point $$(x, y)$$?

Accepted Answer

The $$y-$$coordinate

Question 13

If a segment has endpoints $$(-3, 4)$$ and $$(5, -2)$$, what is the midpoint?

Accepted Answer

$$(1, 1)$$

Question 14

A cell phone tower is located at $$(0, 0). A $$user is at $$(3, 4). $$What is the user's distance from the tower?

Accepted Answer

$$5$$

Question 15

Which of the following points lies in Quadrant IV?

Accepted Answer

$$(5, -2)$$

Question 16

A triangle has vertices at $$A(-3, 1)$$, $$B(-3, 4)$$, and $$C(4, 1). $$What is the area of the triangle?

Accepted Answer

$$10.5$$

Question 17

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 18

A delivery robot starts at $$(1, 2)$$ and moves to $$(7, 8). $$What is the total distance traveled if it moves first horizontally, then vertically?

Accepted Answer

$$12$$

Question 19

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

Accepted Answer

The axes are always at a $$45^\circ$$ angle to each other.

Question 20

A wildlife biologist tracks two animals at $$(2, 5)$$ and $$(8, 11). $$What is the straight-line distance between them?

Accepted Answer

$$6\sqrt{2}$$

Graphs: The Distance and Midpoint Formulas in the Rectangular Coordinate System

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