PLOTTING POINTS ON A COORDINATE PLANE

What is Coordinate plane?

The two dimensional plane is called the Cartesian Plane, or the Coordinate Plane and the axes are called the coordinate axes or x-axis and y-axis.

Plot the point in a coordinate plane. Describe the location of the point.

Problem 1 :

Solution :

a)

• Start at 0 and move 4 units to the right.
• Then move 1 unit upward.

Now, Point A(4, 1) is in Quadrant I.

b)

• Start at 0 and move 3 units downward.

Now, Point B(0, -3) is on the y-axis.

c)

• Start at 0 and move 2 units to the left.
• Then move 5 units downward.

Now, Point C(-2, -5) is in Quadrant III.

d)

• Start at 0 and move 1 unit to the left.
• Then move 1 unit upward.

Now, Point P(-1, 1) is in Quadrant II.

e)

• Start at 0 and move 4 units to the right.
• Then move 5 units downward.

Now, Point Q(4, -5) is in Quadrant IV.

f)

Now, Point R(0, 0) is located at the origin.

g)

Now, Point B(-2, 0) is on the x-axis.

Problem 2 :

Which ordered pair corresponds to point T?

a) (−3, −3)      b) (−3, 3)      c) (3, −3)      d) (3, 3)

Solution :

Point T is 3 units to the right of the origin and 3 units down. So, the x-coordinate is 3 and the y-coordinate is −3. The ordered pair (3, −3) corresponds to point T. The correct answer is c.

Problem 3 :

Plot

(a) (−4, 2) and (b) (0, −3)

in a coordinate plane. Describe the location of each point.

Solution :

a) Start at the origin. Move 4 units left and 2 units up. Then plot the point. The point is in Quadrant II.

b) Start at the origin. Move 3 units down. Then plot the point. The point is on the y-axis.

Problem 4 :

You and a friend have tickets to see a game in Tampa, Florida. You sit in the Ship Section and your friend sits at (−4, −2).

a. Write an ordered pair for your location. In which quadrant are you seated?

b. In which quadrant is your friend seated?

c. A fan in Quadrant II is chosen to win a prize. Do you or your friend have a chance to win the prize?

Solution :

a. The Ship Section is 6 units to the right of the origin and 1 unit down. So, your seat is located at (6, −1). You are seated in Quadrant IV.

b. Move 4 units to the left of the origin and 2 units down. Your friend is seated in Quadrant III.

c. You are seated in Quadrant IV and your friend is seated in Quadrant III. So, you and your friend do not have a chance to win the prize.

Problem 5 :

How many quadrants are in a coordinate plane?

Solution :

There are four quadrants in the coordinate plane.

Problem 6 :

Is the point (0, −7) on the x-axis or the y-axis?

Solution :

Every point can be represented in the form (x, y). Here x = 0 and y = -7

Since the value of x-coordinate is 0, then the point should lie on the y-axis. 

Problem 7 :

How are the locations of the points (2, −2) and (−2, 2) different?

Solution :

• The point (2, -2) is in the form (x, -y) and it lies in the fourth quadrant.
• The point (-2, 2) is in the form of (-x, y) and it lies in the second quadrant.

Problem 8 :

Describe the characteristics of ordered pairs in each of the four quadrants.

Solution :

The points always can be represented in the form (x co-ordinate, y co-ordinate)

• (x, y) ------> First quadrant
• (-x, y) ------> Second quadrant
• (-x, -y) ------> Third quadrant
• (x, -y) ------> Fourth quadrant

Problem 9 :

The coordinate of three vertices of square are shown in the figure. What are the coordinates of the fourth vertex ?

Solution :

Let the point A(-2, -4), B(3, -4), C(3, 1) and D be the unknown.

• Horizontal distance between the points (-2, -4) and (3, -4) is 5 units
• Vertical distance between the points (3, -4) and (3, 1) is 5 units.

Since after connecting all he points, we get the shape square. The horizontal and vertical distance between the points (3, 1) and unknown point should be the same.

So, the required point is (-2, 1).

Problem 10 :

The points D(1, 1), E(1, −2), F(−2, −2), and G(−2, 1) are vertices of a figure.

a. Draw the figure in a coordinate plane.

b. Find the perimeter of the figure.

c. Find the area of the figure.

Solution :

a) Ploting the points in the coordinate plane.

b. Side length of square = 6 units

Perimeter of square = 4(6)

= 24 units

c. Area of square = a²

= 6²

= 36 square units