Plotting Points

Show your work for each problem.

1.
In the ordered pair , which number tells you how far to move horizontally?
1. a)5
2. b)3
3. c)8
4. d)2
Answer: 5
In , the first number is the x-coordinate, which tells you to move 5 units horizontally (to the right).
2.
What are the coordinates of the origin?
1. a)
2. b)
3. c)
4. d)
Answer:
The origin is at . This is the center of the coordinate plane where the x-axis and y-axis intersect.
3.
For the point , how many units do you move to the right?
Answer: 7
The x-coordinate is , so you move 7 units to the right. Positive x means right, negative x means left.
4.
For the point , how many units do you move up?
Answer: 9
The y-coordinate is , so you move 9 units up. Positive y means up, negative y means down.
5.
In which quadrant is the point ?
1. a)Quadrant II
2. b)Quadrant I
3. c)Quadrant IV
4. d)Quadrant III
Answer: Quadrant I
has both positive coordinates. Quadrant I is the top-right quadrant where both x and y are positive.
6.
In which quadrant is the point ?
1. a)Quadrant III
2. b)Quadrant I
3. c)Quadrant IV
4. d)Quadrant II
Answer: Quadrant II
x is negative () so move left. y is positive () so move up. Left and up = Quadrant II (-, +).
7.
For the point , in which direction do you move for the x-coordinate? (Write 'left' or 'right')
Answer: left
A negative x-coordinate means move LEFT. The x-coordinate tells you to move 5 units to the left of the origin.
8.
The point lies on which axis? (Write 'x-axis' or 'y-axis')
Answer: y-axis
When , the point lies on the y-axis. You don't move horizontally, only vertically to 8 units up.
9.
Plot the point . Describe each step.
Answer: (-3, -4)
1. Where do you always start when plotting a point? origin
2. The x-coordinate is . Which direction do you move? left
3. How many units do you move left? 3
4. The y-coordinate is . Which direction do you move? down
5. In which quadrant is this point? III
10.
A treasure is hidden at coordinates . Describe how to find it from the origin.
Answer: 6 right, 2 down
1. What is the x-coordinate of the treasure? 6
2. Is the x-coordinate positive or negative? positive
3. So you move right or left first? right
4. What is the y-coordinate? -2
5. So you move up or down? down
6. Which quadrant contains the treasure? IV
11.
Which point lies on the x-axis?
1. a)
2. b)
3. c)
4. d)
Answer:
A point lies on the x-axis when . Only has . The point lies on the y-axis instead.
12.
A character at moves 5 units left and 4 units up. What is the new x-coordinate?
Answer: -2
Starting x is . Moving 5 units left means subtracting 5: . The new x-coordinate is .
13.
Order these points from left to right on the coordinate plane: , , ,
Answer: (-4, 1), (-1, 2), (0, 3), (2, 5)
1. Which coordinate determines left-right position? x
2. What are the x-coordinates? List them: 2, -4, 0, -1 -4, -1, 0, 2
3. Which point is furthest left? (-4, 1)
4. Which point is furthest right? (2, 5)
14.
If you reflect the point across the x-axis, what is the new point?
Answer: (4, 3)
1. When reflecting across the x-axis, which coordinate changes? y
2. The original x-coordinate is 4. What is the new x-coordinate? 4
3. The original y-coordinate is . What is its opposite? 3
4. Write the reflected point as (x, y): (4, 3)
15.
Point A is at and Point B is at . What is the distance between them? (Just the number)
Answer: 6
Since both points have , they are on a vertical line. Distance = units.
16.
A rectangle has corners at , , , and . What is the perimeter of this rectangle?
Answer: 14
1. What is the width (horizontal distance) between and ? 4
2. What is the height (vertical distance) between and ? 3
3. Perimeter = 2(width) + 2(height). Calculate: 14