MENU
❌
Home
Math Forum/Help
Problem Solver
Practice
Algebra
Geometry
Tests
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
Trigonometry
Trigonometry
Identities
Trigonometry
Trigonometric Inequalities
Extremal value problems
Numbers Classification
Geometry
Intercept Theorem
Slope
Law of Sines
Law of Cosines
Vectors
Probability
Limits of Functions
Properties of Triangles
Pythagorean Theorem
Matrices
Complex Numbers
Inverse Trigonometric Functions
Analytic Geometry
Analytic Geometry
Circle
Parabola
Ellipse
Conic sections
Polar coordinates
Integrals
Integrals
Integration by Parts
Trigonometric Substitutions
Application
Differential Equations
Home
Practice
The Coordinate Plane
Easy
Normal
Difficult
The Coordinate Plane: Difficult Problems with Solutions
By Catalin David
Problem 1
If point A with the coordinates (2, a) is situated on the x-axis, then
a =
1
-1
0
2
.
Solution:
If point A is on the x-axis, the distance from A to the x-axis is 0, so a = 0.
Problem 2
If point B with the coordinates (a, 3) is situated on the y-axis, then a =
3
-1
1
0
.
Solution:
If point B is on the y-axis, the distance from B to the y-axis is 0, so a = 0.
Problem 3
What are the coordinates of a point found in quadrant II at 4 units from the y-axis and at 2 units from the x-axis?
(-2, 4)
(4, -2)
(-4, 2)
(-4, -2)
Solution:
Since the point is found in quadrant II, its first coordinate is negative and its second coordinate is positive. Since it is at a distance of 4 units from the y-axis, its first coordinate is -4. Since it is at a distance of 2 units from the x-axis, its second coordinate is 2. The coordinates of the point are (-4, 2).
Problem 4
What are the coordinates of a point found in quadrant III at 4 units from the x-axis and at 3 units from the y-axis?
(3, 4)
(-3 , -4)
(-3 , 4)
(3, -4)
Solution:
Since the point is found in quadrant III, both its coordinates are negative. Since it is at a distance of 4 units from the x-axis, its second coordinate is -4. Since it is at a distance of 3 units from the y-axis, its first coordinate is -3. The coordinates of the point are (-3, -4).
Problem 5
What are the coordinates of a point found in quadrant I at 3 units from the x-axis and at 2 units from the y-axis?
(3, 2)
(2, 3)
(-2, 3)
(2, -3)
Solution:
Since the point is found in quadrant I, both its coordinates are positive. Since it is at a distance of 3 units from the x-axis, its second coordinate is 3. Since it is at a distance of 2 units from the y-axis, its first coordinate is 2. The coordinates of the point are (2, 3).
Problem 6
What are the coordinates of a point found in quadrant IV at 1 unit from the y-axis and at 4 units from the x-axis?
(1, 4)
(-1, 4)
(4, -1)
(1, -4)
Solution:
Since the point is found in quadrant IV, its first coordinate is positive and its second coordinate is negative. Since it is at a distance of 1 unit from the y-axis, its first coordinate is 1. Since it is at a distance of 4 units from the x-axis, its second coordinate is -4. The coordinates of the point are (1, -4).
Problem 7
What is the distance between points A(1, 3) and B(4, 3)?
1
4
3
Solution:
Since the points have the same y-coordinate, AB is parallel to the x-axis. The distance between the 2 points is equal to the difference of the x-coordinates. The distance between point A and point B is 4 - 1 = 3 units.
Problem 8
What is the length of AB if A has the coordinates (-3, 2) and B has the coordinates (2, 2)?
-5
-1
5
1
Solution:
The length of AB is equal to the distance from A to B. Since both points have the same y-coordinate, AB is parallel to the x-axis. The length of AB is equal to the difference of the x-coordinates, so 2 - (-3) = 2 + 3 = 5.
Problem 9
What is the length of AB if A has the coordinates (4, 2) and B has the coordinates (4, 6)?
2
6
4
-4
Solution:
The length of AB is equal to the distance from A to B. Since both points have the same x-coordinate, AB is parallel to the y-axis. The length of AB is equal to the difference of the y-coordinates, so 6 - 2 = 4.
Problem 10
What are the coordinates of the symmetric of point A with respect to point B?
(6, 3)
(8, 3)
(3, 8)
(-1, 3)
Solution:
The symmetric of point A with respect to point B is point A', which is found on the same line as A and B. B is halfway between A and A'. The distance from A' to the y-axis is 6 units greater, so its first coordinate is 8. The distance to the x-axis is the same, so the second coordinate of point A' is 3.
The coordinates of point A' are (8, 3).
Problem 11
What is the length of AB if A has the coordinates (-2, -5) and B has the coordinates (-2, 3)?
2
8
-3
7
Solution:
The length of AB is equal to the distance from A to B. Since both points have the same x-coordinate, AB is parallel to the y-axis. The length of AB is equal to the difference of the y-coordinates, so 3 - (-5) = 8.
Problem 12
What is the length of AB if A has the coordinates (-4, 5) and B has the coordinates (-4, -1)?
5
1
6
4
Solution:
The length of AB is equal to the distance from A to B. Since both points have the same x-coordinate, AB is parallel to the y-axis. The length of AB is equal to the difference of the y-coordinates, so 5 - (-1) = 5 + 1 = 6.
Problem 13
What are the coordinates of point B?
(3, 7)
(-1, 3)
(7, 3)
(7, 7)
Solution:
Since point A has the coordinates (3, 3) and AB is horizontal, point B will have the same y-coordinate. Since the length of AB is 4, the x-coordinate of point B is 3 + 4 = 7. Point B has the coordinates (7, 3).
Problem 14
What are the coordinates of point B?
(3, 1)
(-1, 3)
(3, -1)
(3, 6)
Solution:
Since point A has the coordinates (3, 3) and AB is vertical, point B will have the same x-coordinate. Since the length of AB is 4, the y-coordinate of point B is 3 - 4 = -1. Point B has the coordinates (3, -1).
Problem 15
What are the coordinates of point C?
(2, 3)
(3, 2)
(1, 3)
(4, 2)
Solution:
Since AB is horizontal, the y-coordinate of point B is 1 and the x-coordinate is 1 + 2 = 3. Thus, B has the coordinates (3, 1). Since BC is vertical, the x-coordinate of point C is 3 and the y-coordinate is 1 + 1 = 2. Thus, point C has the coordinates (3, 2).
Problem 16
What are the coordinates of point B?
(3, 2)
(2, -8)
(5, 2)
(5, -8)
Solution:
Since all horizontal lines have a length of 1 unit, the x-coordinate of point B is 1 + 4 = 5.
Since all vertical lines have a length of 1 unit, the y-coordinate of point B is -3 + 5 = 2.
Point B has the coordinates (5, 2).
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 - 2021.