Introduction to the Coordinate Plane

Show your work for each problem.

1.
What is the name of the point where the x-axis and y-axis meet?
1. a)Intersection
2. b)Center
3. c)Origin
4. d)Vertex
Answer: Origin
The origin is the special point where the x-axis and y-axis intersect. It has coordinates and serves as the starting point for locating all other points.
2.
Which axis is horizontal?
1. a)y-axis
2. b)origin
3. c)z-axis
4. d)x-axis
Answer: x-axis
The x-axis runs horizontally (left to right). The y-axis runs vertically (up and down).
3.
In the ordered pair , what is the x-coordinate?
Answer: 5
In an ordered pair , the first number is always the x-coordinate. So in , the x-coordinate is .
4.
In the ordered pair , what is the y-coordinate?
Answer: 7
In an ordered pair , the second number is always the y-coordinate. So in , the y-coordinate is .
5.
In which quadrant is the point located?
1. a)Quadrant III
2. b)Quadrant IV
3. c)Quadrant I
4. d)Quadrant II
Answer: Quadrant I
The point has both positive x and positive y coordinates. Quadrant I is where both coordinates are positive (upper right).
6.
In which quadrant is the point located?
1. a)Quadrant II
2. b)Quadrant III
3. c)Quadrant I
4. d)Quadrant IV
Answer: Quadrant II
The point has negative x (left of y-axis) and positive y (above x-axis). This places it in Quadrant II (upper left).
7.
A point is located 6 units to the right and 4 units up from the origin. What is the x-coordinate?
Answer: 6
Moving right means positive x, and moving 6 units right gives . The full coordinates would be .
8.
A point is located 3 units to the left and 5 units down from the origin. What is the y-coordinate?
Answer: -5
Moving down means negative y, and moving 5 units down gives . The full coordinates would be .
9.
Plot the point and identify its quadrant.
Answer: Quadrant IV
1. What is the x-coordinate? Is it positive or negative? 4, positive
2. Which direction do you move for positive x? right
3. What is the y-coordinate? Is it positive or negative? -2, negative
4. Which direction do you move for negative y? down
5. Which quadrant has positive x and negative y? IV
10.
Write the coordinates of a point that is 5 units left and 3 units up from the origin.
Answer: (-5, 3)
1. Is left positive or negative for the x-coordinate? negative
2. What is the x-coordinate for 5 units left? -5
3. Is up positive or negative for the y-coordinate? positive
4. What is the y-coordinate for 3 units up? 3
5. Write the ordered pair (-5, 3)
11.
Which point lies on the x-axis?
1. a)
2. b)
3. c)
4. d)
Answer:
Points on the x-axis have . The point has y-coordinate 0, so it lies on the x-axis.
12.
A point is at . It moves 6 units left and 8 units down. What is the x-coordinate of its new position?
Answer: -4
Starting at and moving 6 units left: . The new position is .
13.
Point starts at . It moves 7 units right and 9 units down. Find the new coordinates of point .
Answer: (4, -5)
1. What is the starting x-coordinate? -3
2. Moving 7 units right means adding 7 to x. Calculate: 4
3. What is the starting y-coordinate? 4
4. Moving 9 units down means subtracting 9 from y. Calculate: -5
5. What are the new coordinates? (4, -5)
14.
Which quadrant does each point belong to: , , ?
Answer: A: IV, B: III, C: II
1. For point : Is x positive or negative? positive
2. For point : Is y positive or negative? negative
3. Point A with (+, -) is in which quadrant? IV
4. For point : Both coordinates are negative. Which quadrant? III
5. For point : x is negative, y is positive. Which quadrant? II
15.
The point is in Quadrant II. What must be true about ? Enter 'positive' or 'negative'.
Answer: negative
Quadrant II contains points with negative x and positive y. Since y = 5 is positive, (the x-coordinate) must be negative.
16.
A game character at must reach the treasure at . How many units right and how many units down must it travel?
Answer: 7 right, 3 down
1. What is the starting x-coordinate? -4
2. What is the ending x-coordinate? 3
3. Calculate the horizontal distance: 7
4. What is the starting y-coordinate? 2
5. What is the ending y-coordinate? -1
6. Calculate the vertical distance: 3