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Quizzes > Mathematics

Coordinate Plane Quadrants: Coordinate System Test

Quick, free coordinate plane quiz with 20 questions. Instant results.

Editorial: Review CompletedCreated By: Madlen DokhoyanUpdated Aug 27, 2025
Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Paper art promoting a Coordinate Plane Challenge trivia quiz for high school students.

This coordinate plane quadrants quiz helps you practice plotting points, reading ordered pairs, and finding quadrants on the grid. Work through 20 Grade 7 questions with instant feedback, then review any misses. Keep building skills with graphing points practice, check your skills in a graphing quiz, or explore a coordinate geometry quiz.

Which quadrant does the point (3, 4) lie in?
Second Quadrant
First Quadrant
Third Quadrant
Fourth Quadrant
The point (3, 4) has both positive x and y coordinates, which places it in the First Quadrant. In the coordinate plane, the first quadrant is where both x and y are positive.
What is the ordered pair for a point with x-coordinate -2 and y-coordinate 5?
(5, -2)
(2, -5)
(-5, 2)
(-2, 5)
An ordered pair is written as (x, y), so with x = -2 and y = 5, the correct written form is (-2, 5). This order matters as it distinguishes the horizontal and vertical coordinates.
Which axis does the point (0, -7) lie on?
x-axis
Neither axis
Origin
y-axis
The point (0, -7) lies on the y-axis because the x-coordinate is 0, and any point with an x-coordinate of 0 lies on the y-axis. This is a fundamental property of the coordinate plane.
What are the coordinates of the origin?
(-1, 0)
(0, 1)
(0, 0)
(1, 1)
The origin is the point where the x-axis and y-axis intersect, which is (0, 0). This is one of the first concepts learned when studying the coordinate plane.
In the coordinate plane, what does the 'x' in an ordered pair (x, y) represent?
The distance from the origin
The vertical position
The horizontal position
The slope of a line
In an ordered pair (x, y), the x-coordinate indicates the horizontal position. This tells you how far left or right a point is from the origin.
Which quadrant does the point (-3, 4) lie in?
First Quadrant
Second Quadrant
Third Quadrant
Fourth Quadrant
The point (-3, 4) has a negative x-coordinate and a positive y-coordinate, placing it in the Second Quadrant. Understanding the signs of coordinates aids in identifying the correct quadrant.
Which of the following points is located in the third quadrant?
(3, -4)
(-3, 4)
(2, 5)
(-2, -5)
In the third quadrant, both coordinates are negative. (-2, -5) is the only option with both x and y negative. This property is essential in recognizing the correct quadrant.
What is the midpoint of the line segment connecting (2, 3) and (8, 11)?
(5, 7)
(4, 7)
(5, 8)
(6, 7)
The midpoint of a segment is found by averaging the x-coordinates and the y-coordinates separately. In this case, (2+8)/2 = 5 and (3+11)/2 = 7, so the midpoint is (5, 7).
How many units is the distance between (1, 2) and (1, 8)?
7 units
5 units
8 units
6 units
Since the x-coordinates are the same, the distance is simply the absolute difference between the y-coordinates. Thus, |8 - 2| = 6 units.
Which point is the reflection of (4, -3) over the x-axis?
(4, -3)
(4, 3)
(-4, 3)
(-4, -3)
When reflecting a point over the x-axis, the x-coordinate remains unchanged while the y-coordinate changes sign. Therefore, the reflection of (4, -3) is (4, 3).
If a point (x, y) is on the line y = 2x + 1, what is y when x = 3?
7
8
5
6
Substituting x = 3 into the equation y = 2x + 1 gives y = 2(3) + 1 = 7. This is a straightforward application of evaluating a linear function.
What is the sum of the x and y coordinates of the point (-4, 9)?
4
13
-5
5
Adding the x-coordinate (-4) and the y-coordinate (9) produces -4 + 9 = 5. This operation tests basic arithmetic with signed numbers.
A line passes through the origin and (2, 5). What is the slope of the line?
5/2
2
3
7
The slope is calculated by dividing the change in y by the change in x: (5 - 0)/(2 - 0) = 5/2. This formula is fundamental in coordinate geometry.
Which coordinate pair is exactly halfway between (0, 0) and (6, -4)?
(3, -2)
(2, -3)
(6, -4)
(3, 2)
The midpoint is found by averaging the corresponding coordinates: (0+6)/2 = 3 and (0+(-4))/2 = -2, so the midpoint is (3, -2). This confirms your understanding of the midpoint formula.
Which of the following points is not located in quadrant I?
(3, 3)
(1, 1)
(4, 5)
(-3, 4)
Quadrant I consists of points with both positive x and y coordinates. (-3, 4) is not in quadrant I, as its x-coordinate is negative, placing it in quadrant II.
Find the distance between the points (2, -1) and (-3, 3) using the distance formula.
√40
5
√29
√41
Using the distance formula, the distance is calculated as √[(2 - (-3))² + (-1 - 3)²] = √(5² + (-4)²) = √(25 + 16) = √41. This formula is a direct application of the Pythagorean theorem.
What is the slope of the line through the points (-2, -3) and (4, 3)?
2
-1
0
1
The slope is found by dividing the difference in y-values by the difference in x-values. In this case, (3 - (-3))/(4 - (-2)) equals 6/6, which simplifies to 1.
The point (x, y) lies on the circle with center (2, 3) and radius 5. Which of the following ordered pairs could NOT be on the circle?
(2, -2)
(7, 3)
(2, 8)
(6, 7)
Plugging each point into the circle's equation (x - 2)² + (y - 3)² = 25 shows that (6, 7) does not satisfy the equation, so it cannot lie on the circle. This exercise checks understanding of the circle equation.
A line parallel to y = 3x - 5 will have the same slope. Which of these lines is parallel to it?
y = 2x - 1
y = x + 7
y = -3x + 4
y = 3x + 4
Parallel lines have identical slopes. Since the slope of y = 3x - 5 is 3, the line y = 3x + 4 is parallel, having the same slope. This demonstrates understanding of the relationship between lines.
Which transformation will move the point (5, -3) to (-1, 4)?
Reflect over the y-axis
Translate by (-6, 7)
Rotate 180 degrees about the origin
Translate by (6, -7)
A translation moves a point by adding a constant vector to it. The vector (-6, 7) takes (5, -3) to (-1, 4), which is the correct transformation. This problem tests understanding of translation vectors.
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Study Outcomes

  1. Identify coordinates of points on the plane.
  2. Plot and interpret positions on the coordinate grid.
  3. Analyze geometric relationships between plotted points.
  4. Solve problems involving distances and midpoints.

Coordinate Plane Quiz - Practice Test Cheat Sheet

  1. Cartesian Coordinate System - Welcome to your math map! The Cartesian plane is made up of a horizontal x-axis and a vertical y-axis that cross at the origin (0,0). Every point is an ordered pair (x,y), like (3, - 2) which means 3 units right and 2 units down.
  2. Plotting Points - Grab your pencil and start at the origin, slide along the x-axis to your x‑value, then move straight up or down to hit the y‑value. It's as easy as "right 4, up 5" for (4,5)! Practicing this will make you a plotting pro in no time.
  3. Four Quadrants - The plane is divided into I, II, III and IV. Each quadrant tells you the sign of x and y: I (+,+), II ( - ,+), III ( - , - ) and IV (+, - ). Knowing this helps you instantly know where a point lives and what its signs should be!
  4. Distance Formula - Imagine connecting two points with a straight "math rope." Use d = √[(x₂‑x₝)² + (y₂‑y₝)²] to measure its length. For example, between (1,2) and (4,6) you get √[(3)²+(4)²] = 5 units.
  5. Midpoint Formula - Want the exact halfway point? Use M = ((x₝+x₂)/2, (y₝+y₂)/2). Between (2,3) and (4,7) you land at (3,5). It's like averaging each coordinate - super handy for bisecting lines.
  6. Slope Calculation - Slope is your line's "rise over run": m = (y₂‑y₝)/(x₂‑x₝). This tells you how steep your line climbs or falls. For (1,2) to (3,6), m = 4/2 = 2, so you rise 2 for every 1 you run.
  7. Slope-Intercept Form - This is y = mx + c, where m is slope and c is the y‑intercept. It's like a line's secret identity: for m=2 and c= - 3 you get y = 2x - 3. Plot the intercept and use slope to draw the rest!
  8. Section (Division) Formula - Divide a line segment in a ratio m:n with P = ((mx₂ + nx₝)/(m+n), (my₂ + ny₝)/(m+n)). It's perfect for splitting paths like a boss - no guessing, just pure math precision.
  9. Triangle Area via Vertices - Compute area with ½|x₝(y₂−y₃) + x₂(y₃−y₝) + x₃(y₝−y₂)|. For (1,2), (4,5) and (6,3) you get 6 square units. It's like plugging into a magic determinant formula!
  10. Parallel & Perpendicular Slopes - Parallel lines share the same slope (m₝ = m₂), while perpendicular ones multiply to - 1 (m₝·m₂ = - 1). So if one line has m=2, its perfect partner stands at m= - ½. Math match made easy!
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