Question 1

Which of the following best describes the point where the two axes intersect on a coordinate plane?

Accepted Answer

The origin

Question 2

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

Accepted Answer

$$2\sqrt{8}$$

Question 3

Which formula correctly gives 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 4

What are the coordinates of the midpoint between $$(−4, −2)$$ and $$(2, 5)$$?

Accepted Answer

$$(−1, 1.5)$$

Question 5

Which quadrant does the point $$(−3, 5)$$ lie in?

Accepted Answer

Quadrant II

Question 6

If the poverty threshold for a family of four was $$15,604 in 1995 and 19$$,716 in 2005, what is the estimated threshold in 2000 using the midpoint formula?

Accepted Answer

$$17,660$$

Question 7

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

Accepted Answer

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

Question 8

A triangle has vertices $$A = (−6, 11)$$, $$B = (3, 9)$$, and $$C = (1, 0). $$Which formula would you use to verify if the triangle is a right triangle?

Accepted Answer

The Pythagorean Theorem: $$a^2$$ + $$b^2$$ = $$c^2$$

Question 9

Which of the following statements is TRUE about the axes on a coordinate plane?

Accepted Answer

The horizontal axis is called the $$x-$$axis and the vertical axis is called the $$y-$$axis.

Question 10

If a point has coordinates $$(0, 4)$$, which axis does it lie on?

Accepted Answer

The $$y-$$axis

Question 11

Given points $$P = (−2, 2)$$ and $$Q = (−5, 8)$$, what is the distance between them?

Accepted Answer

$$\sqrt{45}$$

Question 12

Which of the following best describes an ordered pair $$(x, y)$$?

Accepted Answer

A point in the coordinate plane

Question 13

If the coordinates of a point are $$(x, y)$$ and $$x \u003c 0$$, $$y \u003c 0$$, in which quadrant does the point lie?

Accepted Answer

Quadrant III

Question 14

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

Accepted Answer

It gives the length of the segment between two points.

Question 15

A segment has endpoints $$(a, b)$$ and $$(c, d). $$What are the coordinates of its midpoint?

Accepted Answer

$$\left( \frac{a+c}{2}, \frac{b+d}{2} \right)$$

Question 16

Which of the following best describes the four regions created by the axes on a coordinate plane?

Accepted Answer

Quadrants

The Distance and Midpoint Formulas in the Coordinate Plane

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