MENU
❌
Home
Math Forum/Help
Problem Solver
Practice
Worksheets
Tests
Algebra
Geometry
College Math
History
Games
MAIN MENU
1 Grade
Adding and subtracting up to 10
Comparing numbers up to 10
Adding and subtracting up to 20
Addition and Subtraction within 20
2 Grade
Adding and Subtracting up to 100
Addition and Subtraction within 20
3 Grade
Addition and Subtraction within 1000
Multiplication up to 5
Multiplication Table
Rounding
Dividing
Addition, Multiplication, Division
Perimeter
4 Grade
Adding and Subtracting
Addition, Multiplication, Division
Equivalent Fractions
Divisibility by 2, 3, 4, 5, 9
Area of Squares and Rectangles
Fractions
Equivalent Fractions
Least Common Multiple
Adding and Subtracting
Fraction Multiplication and Division
Operations
Mixed Numbers
Decimals
Expressions
6 Grade
Percents
Signed Numbers
The Coordinate Plane
Equations
Expressions
Polynomials
Symplifying Expressions
Polynomial Vocabulary
Polynomial Expressions
Factoring
7 Grade
Angles
Inequalities
Linear Functions
8 Grade
Congurence of Triangles
Linear Functions
Systems of equations
Slope
Parametric Linear Equations
Word Problems
Exponents
Roots
Quadratic Equations
Quadratic Inequalities
Rational Inequalities
Vieta's Formulas
Progressions
Arithmetic Progressions
Geometric Progression
Progressions
Number Sequences
Reciprocal Equations
Logarithms
Logarithmic Expressions
Logarithmic Equations
Logarithmic Equations
Logarithmic Inequalities
Irrational Equations
Irrational Inequalities
Trigonometry
Trigonometry
Identities
Trigonometry
Trigonometric Equations
Trigonometric Inequalities
Extremal value problems
Numbers Classification
Geometry
Slope
Intercept Theorem
Law of Sines
Law of Cosines
Vectors
Modulus Inequalities
Exponential Inequalities
Exponential Equations
Modulus equations
Probabilities
Functions
Min, Max Values
Limits
Limits of Functions
Monotonicity of Functions
Properties of Triangles
Pythagorean Theorem
Matrices
Complex Numbers
Inverse Trigonometric Functions
Analytic Geometry
Analytic Geometry
Circle
Parabola
Ellipse
Conic sections
Polar coordinates
Derivatives
Derivatives
Applications of Derivatives
Derivatives
Integrals
Integrals
Integration by Parts
Trigonometric Substitutions
Application
Differential Equations
Home
Practice
The Coordinate Plane
Easy
Normal
Difficult
The Coordinate Plane: Problems with Solutions
By
Catalin David
Problem 1
The x-axis is
horizontal
vertical
.
Solution:
Horizontal
Problem 2
The y-axis is
horizontal
vertical
.
Solution:
Vertical
Problem 3
How many coordinates does any point in a plane have?
1
2
3
4
Solution:
2
Problem 4
The first coordinate of the point is called
x
y
.
Solution:
The x coordinate, which is always on the x-axis.
Problem 5
The second coordinate of the point is
x
y
.
Solution:
The y coordinate, which is always on the y-axis.
Problem 6
The x coordinate of a point in a plane represents
the distance from the point to the x-axis
the distance from the point to the y-axis
.
Solution:
The distance from the point to the y-axis.
Problem 7
The y coordinate of a point in a plane represents
the distance from the point to the x-axis
the distance from the point to the y-axis
.
Solution:
The distance from the point to the x-axis.
Problem 8
How many points on the y-axis are at a distance of 3 units from the x-axis?
1
2
Solution:
If the points are on the y-axis, their first coordinate is 0. If the points are at a distance of 3 units from the x-axis, their second coordinate can be 3 or -3. There are two points which fulfill both conditions: B(0, 3) and B'(0, -3).
Problem 9
How many points on the x-axis are at a distance of 2 units from the y-axis?
1
2
Solution:
If the points are on the x-axis, their second coordinate is 0. If the points are at a distance of 2 units from the y-axis, their first coordinate can be 2 or -2. There are two points which fulfill both conditions: A(2, 0) and A'(-2, 0).
Problem 10
How many quadrants are formed by the x- and y-axes in a plane?
2
4
1
6
Solution:
4
Problem 11
The coordinates of the point where the x- and y-axes meet are
(0, 0)
(0, 1)
(1, 0)
(-1, 1)
.
Solution:
(0, 0)
Problem 12
What are the signs of the two coordinates of point A?
(-, +)
(-, -)
(+, +)
(+, -)
Solution:
Point A is found in quadrant I,
so both its coordinates are positive.
Problem 13
What are the signs of the two coordinates of point B?
(-, -)
(+, +)
(+, -)
(-, +)
Solution:
Point B is found in quadrant IV,
so its x-coordinate is positive and
its y-coordinate is negative.
Problem 14
What are the signs of the two coordinates of point C?
(+, -)
(-, -)
(+, +)
(-, +)
Solution:
Point C is found in quadrant II,
so its x-coordinate is negative and
its y-coordinate is positive.
Problem 15
What are the signs of the two coordinates of point D?
(+, -)
(-, -)
(+, +)
(-, +)
Solution:
Point D is found in quadrant III,
so both its coordinates are negative.
Problem 16
Which quadrant contains point A (-1, -1)?
II
IV
III
I
Solution:
Since both its coordinates are negative, point A is in quadrant III.
Problem 17
Which quadrant contains point B (-2, 1)?
I
II
III
IV
Solution:
Since its first coordinate is negative and the second one is positive, point B is in quadrant II.
Problem 18
What are the coordinates of point A?
(2, 1)
(1, 2)
(2, 2)
(1, 1)
Solution:
The coordinates of point A are (2, 1), since it is found in quadrant I at a distance of 2 units of length from the y-axis and 1 unit from the x-axis.
Problem 19
What are the coordinates of point B?
(2, 3)
(3, -2)
(-2, 3)
(-2, -3)
Solution:
The coordinates of point B are (-2, 3), since it is found in quadrant II at a distance of 2 units of length from the y-axis and 3 units from the x-axis.
Problem 20
What are the coordinates of point C?
(-4, 3)
(3, -4)
(-3, 4)
(-3, -4)
Solution:
The coordinates of point C are (3, -4), since it is found in quadrant III at a distance of 3 units of length from the y-axis and 4 units from the x-axis.
Problem 21
What are the coordinates of point D?
(1, -1)
(1, 1)
(-1, 1)
(-1, -1)
Solution:
The coordinates of point D are (-1, -1), since it is found in quadrant IV at a distance of 1 units of length from the Y-axis and 1 unit from the x-axis.
Problem 22
What are the coordinates of point A?
(0, 3)
(3, 3)
(-3, 0)
(3, 0)
Solution:
Point A is right on the x-axis, so its y-coordinate is 0. A is at a distance of 3 units to the right of the y-axis, so its x-coordinate is 3. Thus, the coordinates of point A are (3, 0).
Problem 23
What are the coordinates of point B?
(-2, 0)
(0, -2)
(0, 2)
(1, 1)
Solution:
Point B is right on the y-axis, so its x-coordinate is 0. B is at a distance of 2 units from the x-axis, so its y-coordinate is 2. Thus, the coordinates of point B are (0, -2).
Problem 24
Which point has the coordinates (-3, 4)?
A
B
C
D
Solution:
Answer: A
Problem 25
What is the length of BC?
2
3
6
4
Solution:
Since points B and C have the same y-coordinate, the length of BC is equal to the difference of the distances from the two points to the y-axis. The coordinates of B are (3, 2) and those of C are (6, 2). B is at a distance of 3 units from the y-axis and C is at a distance of 6 units from the y-axis. Thus, the length of BC is 6 - 3 = 3 units.
Problem 26
What is the length of BC?
3
2
4
5
Solution:
Since points B and C have the same x-coordinate, the length of BC is equal to the difference of the distances from the two points to the x-axis. The coordinates of B are (3, 2) and those of C are (3, 4). B is at a distance of 2 units from the x-axis and C is at a distance of 4 units from the x-axis. Thus, the length of BC is 4 - 2 = 2 units.
Problem 27
What is the length of AB?
3
2
5
1
Solution:
Since point A's coordinates are (4, 3), the distance from A to the x-axis is 3 units. Since point B's coordinates are (4, -2), the distance from B to the x-axis is 2 units. The length of AB is 3 + 2 = 5 units.
Problem 28
What is the length of AB?
3
9
6
8
Solution:
Since point A's coordinates are (-3, 1), the distance from A to the y-axis is 3 units. Since point B's coordinates are (6, 1), the distance from B to the y-axis is 6 units. The length of AB is 3 + 6 = 9 units.
Problem 29
What is the perimeter of rectangle ABCD?
6
10
12
15
Solution:
The perimeter of a rectangle is 2L + 2l (= 2AB + 2BC).
Since point A's coordinates are (2, 3), the distance from A to the y-axis is 2 units. Since point B's coordinates are (6, 3), the distance from B to the y-axis is 6 units. Thus, AB = 6 - 2 = 4 units.
Since point C's coordinates are (6, 1), the distance from C to the x-axis is 1 unit and the distance from B to the x-axis is 3. Thus, BC = 3 - 1 = 2 units.
P = $2 \cdot 4 + 2 \cdot 2 = 8 + 4 = 12$
Problem 30
What are the coordinates of the symmetric of A with respect to the x-axis?
(-2, 3)
(2, -3)
(-2, -3)
Solution:
The symmetric of point A with respect to the x-axis is at the same distance from the x-axis as A. Thus, its second coordinate is -3, the first coordinate remaining the same. The coordinates of the point are (2, -3).
Problem 31
What are the coordinates of the symmetric of point A with respect to the y-axis?
(2, -3)
(-2, -3)
(-2, 3)
Solution:
The symmetric of point A with respect to the y-axis is at the same distance from the y-axis as A. Thus, its first coordinate is -2, the second coordinate remaining the same. The coordinates of the point are (-2, 3).
Problem 32
If point A moved 2 units higher, what would its coordinates be?
(5, 2)
(4, 3)
(2, 5)
(2, 1)
Solution:
If point A moved 2 units higher, its y-coordinate would be 3 + 2 = 5. The x-coordinate would remain the same. The new coordinates would be (2, 5).
Problem 33
If point B moved 2 units higher, what would its coordinates be?
(3, -6)
(5, -4)
(3, -2)
(3, -4)
Solution:
If point B moved 2 units higher, its y-coordinate would be -4 + 2 = -2. The x-coordinate would remain the same. The new coordinates would be (3, -2).
Problem 34
If point A moved 1 unit lower, what would its coordinates be?
(1, 3)
(2, 2)
(1, 2)
(4, 2)
Solution:
If point A moved 1 unit lower, its y-coordinate would be 3 - 1 = 2. The x-coordinate would remain the same. The new coordinates would be (2, 2).
Problem 35
If point B moved 2 units lower, what would its coordinates be?
(1, -4)
(1, -6)
(3, -6)
Solution:
If point B moved 2 units lower, its y-coordinate would be -4 - 2 = -6. The x-coordinate would remain the same. The new coordinates would be (3, -6).
Problem 36
If point A moved 3 units to the left, what would its coordinates be?
(2, 0)
(-1, 0)
(-1, 3)
Solution:
If point A moved 3 units to the left, its x-coordinate would be 2 - 3 = -1. The y-coordinate would remain the same. The new coordinates would be (-1, 3).
Problem 37
If point B moved 2 units to the right, what would its coordinates be?
(3, -2)
(5, -4)
(5, -2)
(1, -4)
Solution:
If point B moved 2 units to the right, its x-coordinate would be 3 + 2 = 5. The y-coordinate would remain the same. The new coordinates would be (5, -4).
Easy
Normal
Difficult
Submit a problem on this page.
Problem text:
Solution:
Answer:
Your name(if you would like to be published):
E-mail(you will be notified when the problem is published)
Notes
: use [tex][/tex] (as in the forum if you would like to use latex).
Correct:
Wrong:
Unsolved problems:
Contact email:
Follow us on
Twitter
Facebook
Copyright © 2005 - 2022.