Question 1

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

Accepted Answer

$$x \u003c 0, y \u003c 0$$

Question 2

What is the distance between the points $$A(2, 3)$$ and $$B(-1, 7) in $$the Cartesian plane?

Accepted Answer

$$\sqrt{32}$$

Question 3

The midpoint of the segment joining the points $$P(4, -2)$$ and $$Q(-6, 8) is$$:

Accepted Answer

$$(0, 3)$$

Question 4

If a point has coordinates $$(a, 0)$$, where is it located in the Cartesian plane?

Accepted Answer

On the x-axis

Question 5

Which formula is used to find the distance $$d$$ between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Question 6

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

Accepted Answer

$$6$$

Question 7

Which of the following statements about the distance between two points is correct?

Accepted Answer

The distance is always positive unless the points are identical.

Question 8

If the midpoint of a segment is $$(5, -2)$$ and one endpoint is $$(3, 4)$$, what are the coordinates of the other endpoint?

Accepted Answer

$$(7, -8)$$

Question 9

A city park is represented by the points $$(1, 2)$$ and $$(5, 6) on a $$map. What is the midpoint of the park?

Accepted Answer

$$(3, 4)$$

Question 10

Which of the following is NOT a property of the midpoint formula?

Accepted Answer

The midpoint is always at the origin.

Question 11

A medical drone must travel from $$(2, 5) to$$ $$(7, 9). $$What is the straight-line distance it must cover?

Accepted Answer

$$\sqrt{41}$$

Question 12

Which quadrant contains points where the x-coordinate is positive and the y-coordinate is negative?

Accepted Answer

Quadrant IV

Question 13

If a point is located at $$(0, b)$$, where $$b 
eq 0$$, which axis is it on?

Accepted Answer

y-axis

Question 14

A right triangle is formed by the points $$(1, 1)$$, $$(1, 4)$$, and $$(5, 1). $$What is the length of the hypotenuse?

Accepted Answer

$$5$$

Question 15

Which step is necessary to show that a triangle is a right triangle using the distance formula?

Accepted Answer

Show that the square of the length of one side equals the sum of the squares of the other two sides.

Question 16

A wildlife biologist marks two locations at $$(3, -2)$$ and $$(-1, 4). $$What is the distance between these locations?

Accepted Answer

$$\sqrt{52}$$

Question 17

If the coordinates of the origin are $$(0, 0)$$, which statement is true?

Accepted Answer

The origin is not in any quadrant.

Question 18

Which of the following is the correct formula for the midpoint $$M$$ between $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Question 19

A delivery truck travels from $$(0, 0) to$$ $$(6, 8). $$What is the distance covered?

Accepted Answer

$$10$$

Graphs: The Distance and Midpoint Formulas

Guida di studio - Domande di pratica