Identifying Quadrants

Show your work for each problem.

1.
In which quadrant is the point ?
1. a)Quadrant III
2. b)Quadrant II
3. c)Quadrant IV
4. d)Quadrant I
Answer: Quadrant I
Both and are positive. Points with coordinates are in Quadrant I (upper right).
2.
In which quadrant is the point ?
1. a)Quadrant III
2. b)Quadrant IV
3. c)Quadrant I
4. d)Quadrant II
Answer: Quadrant III
Both and are negative. Points with coordinates are in Quadrant III (lower left).
3.
A point has coordinates . Enter the quadrant number (1, 2, 3, or 4).
Answer: I
With and , both coordinates are positive. This places the point in Quadrant I.
4.
A point has coordinates . Enter the quadrant number (1, 2, 3, or 4).
Answer: II
With and , we have . This is Quadrant II (upper left).
5.
Which quadrant has points with negative x and negative y coordinates?
1. a)Quadrant III
2. b)Quadrant II
3. c)Quadrant IV
4. d)Quadrant I
Answer: Quadrant III
Quadrant III (lower left) contains all points where both x and y are negative .
6.
Determine which quadrant contains the point .
Answer: IV
1. What is the sign of the x-coordinate (5)? positive
2. What is the sign of the y-coordinate (-4)? negative
3. Which quadrant has ? Enter the number. 4
7.
The point is located:
1. a)In Quadrant IV
2. b)In Quadrant III
3. c)On the x-axis
4. d)On the y-axis
Answer: On the y-axis
When , the point is on the y-axis. Points on the axes are not in any quadrant.
8.
A point has coordinates . Enter the quadrant number (1, 2, 3, or 4).
Answer: 4
With and , we have . This places the point in Quadrant IV.
9.
In which quadrant is the point ?
Answer: II
1. Is x = -7 positive or negative? negative
2. Is y = 3 positive or negative? positive
3. We have . Which quadrant number is upper left? 2
10.
A game character moves from the origin to position . Which quadrant is it in?
Answer: III
1. The character moved left (negative x) or right (positive x)? left
2. The character moved up (positive y) or down (negative y)? down
3. Left and down means which quadrant? III
11.
If a point is in Quadrant IV, which statement is true?
1. a)x < 0 and y > 0
2. b)x > 0 and y < 0
3. c)x < 0 and y < 0
4. d)x > 0 and y > 0
Answer: x > 0 and y < 0
Quadrant IV (lower right) has positive x and negative y: and .
12.
A point has coordinates . Is it in a quadrant? Enter 'yes' or 'no'.
Answer: no
When , the point is on the x-axis. Points on either axis are not in any quadrant.
13.
Point A is in Quadrant I, and Point B is its reflection across the x-axis. In which quadrant is Point B?
Answer: IV
1. What are the signs of Point A's coordinates in Quadrant I? (+, +)
2. When reflecting across the x-axis, which coordinate changes sign? y
3. If Point A has and y changes sign, Point B has what signs? (+, -)
4. Which quadrant has ? IV
14.
A city has latitude (positive) and longitude (positive). If we use latitude as y and longitude as x, which quadrant is this?
Answer: I
1. What is x (longitude)? Is 140°E positive or negative? positive
2. What is y (latitude)? Is 35°N positive or negative? positive
3. We have . Which quadrant? I
15.
Points A and B are in opposite quadrants. If A is at , which could be point B?
1. a)
2. b)
3. c)
4. d)
Answer:
Point A is in Quadrant I . The opposite quadrant is III . Only has both coordinates negative.