Distance and Midpoint Formulas in the Plane flashcards

Question 1

What is the name of the grid system with perpendicular axes that Descartes introduced?

Accepted Answer

The Cartesian coordinate system, also called the rectangular coordinate system.

Question 2

What is the x-axis in the Cartesian coordinate system?

Accepted Answer

The horizontal axis.

Question 3

What is the y-axis in the Cartesian coordinate system?

Accepted Answer

The vertical axis.

Question 4

How are the x-axis and y-axis positioned relative to each other?

Accepted Answer

They are perpendicular to each other.

Question 5

Into how many sections do the two axes divide the coordinate plane?

Accepted Answer

Four sections, called quadrants.

Question 6

What is each of the four sections of the coordinate plane called?

Accepted Answer

A quadrant.

Question 7

In which direction are the quadrants numbered?

Accepted Answer

Counterclockwise.

Question 8

What is the origin of the coordinate plane?

Accepted Answer

The point where the two axes cross, written (0, 0).

Question 9

What are the coordinates of the origin?

Accepted Answer

(0, 0)

Question 10

On the x-axis, which direction holds the positive numbers?

Accepted Answer

To the right of the origin.

Question 11

On the x-axis, which direction holds the negative numbers?

Accepted Answer

To the left of the origin.

Question 12

On the y-axis, which direction holds the positive numbers?

Accepted Answer

Up from the origin.

Question 13

On the y-axis, which direction holds the negative numbers?

Accepted Answer

Down from the origin.

Question 14

What does the x-coordinate of a point tell you?

Accepted Answer

Its horizontal displacement from the origin.

Question 15

What does the y-coordinate of a point tell you?

Accepted Answer

Its vertical displacement from the origin.

Question 16

In what form is an ordered pair written?

Accepted Answer

(x, y), with the x-coordinate first and the y-coordinate second.

Question 17

If the x-coordinate of a point is zero, where does the point lie?

Accepted Answer

On the y-axis.

Question 18

What are the intercepts of a graph?

Accepted Answer

The points at which the graph crosses the axes.

Question 19

What is the x-intercept of a graph?

Accepted Answer

The point at which the graph crosses the x-axis.

Question 20

What is the y-intercept of a graph?

Accepted Answer

The point at which the graph crosses the y-axis.

Question 21

What is the y-coordinate at an x-intercept?

Accepted Answer

Zero.

Question 22

What is the x-coordinate at a y-intercept?

Accepted Answer

Zero.

Question 23

How do you find the x-intercept of an equation?

Accepted Answer

Set y equal to zero and solve for x.

Question 24

How do you find the y-intercept of an equation?

Accepted Answer

Set x equal to zero and solve for y.

Question 25

What does the distance formula find?

Accepted Answer

The distance between two points in the plane.

Question 26

From which theorem is the distance formula derived?

Accepted Answer

The Pythagorean Theorem.

Question 27

What is the distance formula for endpoints (x1, y1) and (x2, y2)?

Accepted Answer

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Question 28

In the distance formula, what does d stand for?

Accepted Answer

The distance between the two points (x1, y1) and (x2, y2).

Question 29

What does the midpoint formula find?

Accepted Answer

The point midway between the two endpoints of a line segment.

Question 30

What is the midpoint formula for endpoints (x1, y1) and (x2, y2)?

Accepted Answer

M = ((x1 + x2)/2, (y1 + y2)/2)

Question 31

In the midpoint formula, what does M stand for?

Accepted Answer

The coordinates of the midpoint of the segment with endpoints (x1, y1) and (x2, y2).

Question 32

In the midpoint formula, how do you get the x-coordinate of the midpoint?

Accepted Answer

Add the two x-coordinates and divide by 2.

Question 33

In the midpoint formula, how do you get the y-coordinate of the midpoint?

Accepted Answer

Add the two y-coordinates and divide by 2.

Question 34

How can the center of a circle be found from the endpoints of a diameter?

Accepted Answer

Take the midpoint of the diameter with the midpoint formula.

Distance and Midpoint Formulas in the Plane flashcards

The cards

How this deck was checked

Sources

Distance and Midpoint Formulas in the Plane flashcards

The cards

How this deck was checked

Sources

More free decks

Human body

Periodic table

Space & physics