Question 1

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

Accepted Answer

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

Question 2

Given the points $$P(2, -1)$$ and $$Q(-4, 3)$$, what is the distance between them?

Accepted Answer

$$\sqrt{36} = 6$$

Question 3

A city wants to build a straight walking path between two parks located at $$(1, 2)$$ and $$(7, 8). $$What is the length of the path, in units?

Accepted Answer

$$6\sqrt{2}$$

Question 4

Which formula gives the midpoint $$M of a $$segment with endpoints $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$)$$?

Accepted Answer

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

Question 5

Find the midpoint of the segment joining $$(-4, 4)$$ and $$(4, 2).$$

Accepted Answer

$$(0, 3)$$

Question 6

A triangle has vertices $$A(-3, 1)$$, $$B(-3, 4)$$, and $$C(4, 1). $$Which side is the longest?

Accepted Answer

$$BC$$

Question 7

Given the triangle with vertices $$A(-3, 1)$$, $$B(-3, 4)$$, and $$C(4, 1)$$, is the triangle a right triangle?

Accepted Answer

Yes, because $$AB^2$$ + $$AC^2$$ = $$BC^2$$

Question 8

If the endpoints of a diameter of a circle are $$(2, 5)$$ and $$(8, 11)$$, what are the coordinates of the center of the circle?

Accepted Answer

$$(5, 8)$$

Question 9

A cell phone tower is located at $$(0, 0). A $$user is at $$(6, 8). $$What is the straight-line distance between the user and the tower?

Accepted Answer

$$10$$

Question 10

Which of the following best describes the geometric meaning of the distance formula?

Accepted Answer

It is derived from the Pythagorean Theorem, representing the hypotenuse of a right triangle formed by the horizontal and vertical distances between two points.

Question 11

A company wants to build a warehouse exactly halfway between two distribution centers at $$(12, 4)$$ and $$(4, 10). $$Where should the warehouse be located?

Accepted Answer

$$(8, 7)$$

Question 12

If the midpoint of a segment is $$(2, -1)$$ and one endpoint is $$(5, 3)$$, what is the other endpoint?

Accepted Answer

$$(-1, -5)$$

Question 13

A drone flies from $$(1, 2) to$$ $$(7, 8)$$, then to $$(7, 2). $$What is the total distance traveled?

Accepted Answer

$$6\sqrt{2} + 6$$

Question 14

Which of the following is NOT a correct application of the midpoint formula?

Accepted Answer

$$M = (x_1$ + x_2$, y_1$ + y_2$)$$

Question 15

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

Accepted Answer

$$24$$

Question 16

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

Accepted Answer

$$8$$

Graphs: The Distance and Midpoint Formulas

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