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
Perimeter
Addition, Multiplication, Division
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
Polynomial Vocabulary
Symplifying Expressions
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: Very Difficult Problems with Solutions
By
Catalin David
Problem 1
What are the coordinates of the symmetric of point A with respect to point O?
(2, -3)
(-2, 3)
(-2, -3)
Solution:
The symmetric of point A with respect to point O is point A', which is found on the same line as A and O. O is halfway between A and A'. Point A is the vertex of a rectangle in quadrant I with a length of 2 and a width of 3 and whose diagonal is OA. Point A' is the vertex of a rectangle of the same size, but in quadrant III and with diagonal OA'. The coordinates of point A' are (-2, -3).
Problem 2
What are the coordinates of M, found halfway between A and B?
(3, 4.5)
(4.5, 3)
(6, 3)
Solution:
AB is parallel to the x-axis and has a length of 7 - 2 = 5 units. The length of AM is equal to half of the length of AB = 2.5 units. The coordinates of point M are (2 + 2.5, 3) = (4.5, 3).
Problem 3
Square OCAB has an area of 9 square units. Point O is found where the axes meet. What are the coordinates of point A?
(9, 3)
(3, 1)
(3, 3)
(2, 2)
Solution:
If the square has an area of 9 square units, then its side has a length of 3 units. If O is where the axes meet, then points C and B are found on the x- and y-axes and they have the coordinates (3, 0) and (0, 3). Point A is at 3 units from the x-axis and at 3 units from the y-axis and it has the coordinates (3, 3).
Problem 4
How many points are found on the circle whose center is O, having a radius of 2 units?
2
6
8
4
Solution:
The points which are found on the circle must be at a distance of 2 units from O. The points which fulfill this condition are A, D, G and J. The others are at a distance greater than 2 from point O.
Problem 5
The area of triangle ABC is
5
6
4
3
.
Solution:
Triangle ABC can be included inside square MOCN. We can express the area of the triangle as the difference between the area of the square and the area of the 3 right triangles. The area of square MOCN is 9 square units. The area of triangle AMB is 2 square units. The area of triangle BOC is 1.5 square units. The area of triangle CAN is 1.5 square units. Thus, the area of triangle ABC is 9 - (2 + 1.5 + 1.5) = 9 - 5 = 4 square units.
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:
Feedback
Contact email:
Follow us on
Twitter
Facebook
Copyright © 2005 - 2022.