OPENING ACTIVITY

Using the words below, try to determine what we’ll be talking about in today’s lesson.

x-axis quadrantsorigin y-axis

LG 607: STUDENTS WILL BE ABLE TO APPLY AND EXTEND PREVIOUS

UNDERSTANDINGS OF NUMBERS TO THE SYSTEM OF RATIONAL NUMBERS.

THE COORDINATE PLANE

The Coordinate Plane

Coordinate plane: A two-dimensional system for graphing ordered pairs, formed by two perpendicular number lines intersecting at their zero points and creating four quadrants.

x-axis

y-axis

The Coordinate Plane

A trick to remember the four quadrants: Think of the letter C. The way the boxes are touched by drawing the letter C is the way we number the quadrants.

CIII

III IV

THINK – PAIR - SHARE

All points on the coordinate plane are described with reference to the origin. What is the origin, and what are its coordinates?

Origin(0, 0)

Write this down…

To describe locations of points in the coordinate plane we use_______________ of numbers.

Order is important, so on the coordinate plane we use the form (_____).

The first coordinate represents the point’s location from zero on the ___-axis, and the second coordinate represents the point’s location from zero on the ___-axis.

ordered pairs

x , y

x

y

Let’s Practice

Use the coordinate plane below to answer parts (a)–(c).

a. Graph at least five points on the 𝑥-axis and label their coordinates.

b. What do the coordinates of your points have in common?

c. What must be true about any point that lies on the 𝑥-axis? Explain.

Let’s Practice

Use the coordinate plane below to answer parts (a)–(c).

a. Graph at least five points on the y-axis and label their coordinates.

b. What do the coordinates of your points have in common?

c. What must be true about any point that lies on the y-axis? Explain.

Graphing Ordered Pairs

Locate and label each point described by the ordered pairs below. Indicate which of the quadrants the points lie in.

a. (7,2)

b. (3,−4)

c. (1,−5)

d. (−3,8)

e. (−2,−1)

The Four Quadrants

BRAIN BREAK

https://www.youtube.com/watch?v=019n3lfLUzI&list=PL404D7D67ADE6A3D2&index=5

Distance on the Coordinate Plane

Four friends are touring on motorcycles. They come to an intersection of two roads; the road they are on continues straight, and the other is perpendicular to it. The sign at the intersection shows the distances to several towns. Draw a map/diagram of the roads and use it and the information on the sign to answer the following questions:

Distance on the Coordinate Plane

Where would each city be

located on this grid?

Distance on the Coordinate Plane

What is the distance between Albertsville and Dewey Falls?

What is the distance between Blossville and Cheyenne?

Albertsville

Dewey Falls

Blossville

Cheyenne

14 miles

9 miles

Distance on the Coordinate Plane

Consider the points (−4,0) and (5,0). What do the ordered pairs have in common and what does that mean about their location in the coordinate plane?

How did we find the distance between two numbers on the number line?

Both of their -coordinates are zero so each point lies on 𝒚the -axis, the horizontal number line. 𝒙

We calculated the absolute values of the numbers, which told us how far the numbers were from zero. If the numbers were located on opposite sides of zero, then we added their absolute values together. If the numbers were located on the same side of zero, then we subtracted their absolute values.

Distance on the Coordinate Plane

Consider the line segment with endpoints (− , ) and 𝟑 𝟑(− ,− ). 𝟑 𝟓What do the endpoints, which are represented by the ordered pairs, have in common?

What does that tell us about the location of the line segment on the coordinate plane?

Find the length of the line segment by finding the distance between its endpoints.

Both have the same x-coordinate.

The endpoints create a vertical line segment.

The endpoints are on the same vertical line, so we only need to find the distance between and − on the number line. | |= 𝟑 𝟓 𝟑 𝟑and |− |= , and the numbers are on opposite sides of zero, so 𝟓 𝟓the values must be added: + = . So, the distance between 𝟑 𝟓 𝟖(− , ) and (− ,− ) is units. 𝟑 𝟑 𝟑 𝟓 𝟖

Homework

Plotting points (Page 409 in your book)Draw a coordinate gridPlot the following points(3,2), (8,4), (−3,8), (−2,−9), (0,6), (−1,−2), (10,−2) Due Wednesday (White)