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Quizzes > Mathematics > Geometry

Take the Cartesian Plane Questions & Answers Quiz

Think you can ace these coordinate plane questions? Dive in!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration of Cartesian plane grid with plotted points axes lines and geometric shapes on dark blue background

Use this Cartesian plane quiz to practice plotting points, naming quadrants, and reading coordinates on a grid. You'll build speed and spot gaps before a test. If you want a quick refresher first, see points, lines, and planes, then sharpen skills with more graph practice.

Which quadrant does the point (-3, 4) lie in?
Quadrant IV
Quadrant I
Quadrant III
Quadrant II
The Cartesian coordinate plane is divided into four quadrants. Points with a negative x-value and a positive y-value lie in Quadrant II. Since (-3, 4) has x negative and y positive, it is located in Quadrant II. For more information, visit .
On the Cartesian plane, which ordered pair is located 2 units to the right of the origin and 5 units down?
(2, 5)
(2, -5)
(-2, -5)
(-2, 5)
Moving 2 units to the right adds 2 to the x-coordinate, and moving 5 units down subtracts 5 from the y-coordinate. Therefore, the point is (2, -5). This is a basic use of plotting relative to the origin. More details at .
What are the coordinates of the origin in the Cartesian plane?
(0, 0)
(1, 0)
(1, 1)
(0, 1)
The origin is the point where the x-axis and y-axis intersect. By definition, it has coordinates (0, 0). All other points are described relative to this central point. See for more on the origin.
Which of the following points lies on the x-axis?
(-2, 5)
(0, 4)
(-1, 1)
(3, 0)
A point lies on the x-axis when its y-coordinate is zero. All points of the form (x, 0) are on the x-axis. Since (3, 0) has y = 0, it is on the x-axis. More examples are available at .
What is the distance between the points (1, 2) and (4, 6)?
10
7
?13
5
The distance formula is ?[(x? - x?)² + (y? - y?)²]. Substituting gives ?[(4 - 1)² + (6 - 2)²] = ?[3² + 4²] = 5. This is a standard 3-4-5 right triangle. See for more.
Find the midpoint of the segment joining (-2, -4) and (6, 8).
(2, 2)
(-4, -4)
(1, 1)
(4, 4)
The midpoint formula is ((x? + x?)/2, (y? + y?)/2). Calculating gives ((-2 + 6)/2, (-4 + 8)/2) = (2, 2). This point is exactly halfway between the endpoints. For a deeper look, visit .
Which equation represents the vertical line that passes through x = 3?
3x + y = 0
x = 3
y = x + 3
y = 3
Vertical lines have equations of the form x = constant. The constant is the x-coordinate of every point on the line. Thus x = 3 is the correct representation. More on vertical lines at .
What is the reflection of the point (2, 5) across the y-axis?
(-2, 5)
(-2, -5)
(2, -5)
(5, 2)
Reflecting over the y-axis changes the sign of the x-coordinate only. The y-coordinate remains the same. Therefore (2, 5) becomes (-2, 5). See more at .
What is the slope of the line passing through (-3, 1) and (2, -4)?
-5
1
5
-1
Slope is (y? - y?)/(x? - x?). Here that is (-4 - 1)/(2 - (-3)) = -5/5 = -1. A negative slope indicates a descending line from left to right. For more, visit .
At what point do the lines y = 2x + 1 and y = -x + 4 intersect?
(-1, 3)
(1, 3)
(2, 5)
(1, -1)
Set 2x + 1 = -x + 4 and solve: 3x = 3, so x = 1. Substituting gives y = 2(1) + 1 = 3. Thus the intersection is (1, 3). See for more.
Which describes the solution set of the inequality y > -x + 2 on the Cartesian plane?
The region below the line y = -x + 2
The region to the left of the line y = -x + 2
The region above the line y = -x + 2
The region on the line y = -x + 2
An inequality y > mx + b includes points whose y-coordinate is greater than the line's value. Thus the graph shows all points above the line y = -x + 2 (not including the boundary). A dashed line is often used to show the boundary is not included. More detail at .
Find the area of the triangle with vertices A(0, 0), B(4, 0), and C(0, 3) in the Cartesian plane.
7
6
12
8
The base lies along the x-axis from (0, 0) to (4, 0), so its length is 4. The height is the y-coordinate of point C, which is 3. The area formula is ½ × base × height = ½ × 4 × 3 = 6. For a coordinate-based approach, see .
0
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Study Outcomes

  1. Plot Points with Precision -

    Learn to place ordered pairs accurately on the Cartesian grid by interpreting the x- and y-coordinates.

  2. Identify Quadrants Correctly -

    Distinguish the four quadrants on the coordinate plane and determine the sign of each coordinate within them.

  3. Analyze Point Relationships -

    Evaluate distances and spatial relationships between points on the Cartesian plane to solve geometry problems.

  4. Answer Cartesian Plane Questions Confidently -

    Apply strategies for tackling coordinate plane questions and Cartesian grid questions with clarity and accuracy.

  5. Leverage Instant Feedback -

    Use real-time quiz results and explanations to identify mistakes, reinforce concepts, and improve your graphing skills.

Cheat Sheet

  1. Axes and Origin Basics -

    The x-axis (horizontal) and y-axis (vertical) intersect at the origin (0,0), the central reference point for every graph. On your coordinate plane quiz, use the origin to ensure precise plotting and to measure distances to other points.

  2. Plotting Ordered Pairs -

    Coordinates are written as (x,y), with the x-value first and the y-value second. In cartesian plane questions and answers, always respect this order - move x units left/right, then y units up/down when you plot.

  3. Quadrants and Sign Rules -

    Remember "All Students Take Calculus" to identify quadrants: I (+,+), II (−,+), III (−,−), IV (+,−). This mnemonic makes even the trickiest cartesian grid questions feel easy by ensuring you apply the right sign to each coordinate.

  4. Slope-Intercept Form for Lines -

    The equation y = mx + b reveals a line's slope (m) and y-intercept (b) at once. For example, y = 2x − 1 rises 2 units for every 1 unit run and crosses the y-axis at −1 in your graphing points quiz. Mastering this form helps you sketch straight lines quickly and accurately.

  5. Distance and Midpoint Formulas -

    Use the distance formula √[(x₂−x₝)² + (y₂−y₝)²] to find the exact length between two points. The midpoint formula [(x₝+x₂)/2, (y₝+y₂)/2] then gives the center point; for example, between (2,−1) and (−2,3) the midpoint is (0,1). These tools power through any coordinate plane questions with precision.

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