Podcast
Questions and Answers
What are the coordinates of a point located exactly on the x-axis?
What are the coordinates of a point located exactly on the x-axis?
Which of the following statements correctly describes the relationship between coordinate geometry and algebra?
Which of the following statements correctly describes the relationship between coordinate geometry and algebra?
How is the distance between two points represented geometrically in coordinate geometry?
How is the distance between two points represented geometrically in coordinate geometry?
If point A is located at (0, 0) and point B at (36, 15), what is the straight-line distance from A to B?
If point A is located at (0, 0) and point B at (36, 15), what is the straight-line distance from A to B?
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What is the general form of a linear equation in two variables?
What is the general form of a linear equation in two variables?
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What is the value of PQ when points P(3, 2) and Q(-2, -3) are used in the distance formula?
What is the value of PQ when points P(3, 2) and Q(-2, -3) are used in the distance formula?
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Which theorem is applied to confirm that points P, Q, and R form a right triangle?
Which theorem is applied to confirm that points P, Q, and R form a right triangle?
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How can it be determined that points A(1, 7), B(4, 2), C(-1, -1), and D(-4, 4) form a square?
How can it be determined that points A(1, 7), B(4, 2), C(-1, -1), and D(-4, 4) form a square?
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Which of the following expressions correctly represents the distance from point P(x, y) to the origin O(0, 0)?
Which of the following expressions correctly represents the distance from point P(x, y) to the origin O(0, 0)?
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What is the implication if the sum of any two side lengths of a triangle is greater than the third side length?
What is the implication if the sum of any two side lengths of a triangle is greater than the third side length?
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Study Notes
Introduction
- Coordinate geometry uses algebra to study geometrical figures.
- Coordinate geometry is applied in diverse fields.
- Coordinate geometry helps us to find distance between two points.
- Coordinate geometry helps to find coordinates of a point dividing a line segment.
Distance Formula
- The distance formula finds the distance between points without direct measurement.
- The distance between points P(x₁, y₁) and Q(x₂, y₂) is: √( (x₂ - x₁)² + (y₂ - y₁)² )
- The distance of point P(x, y) from origin O(0, 0) is: √(x² + y²)
- The distance formula can be written as: √( (x₁ - x₂)² + (y₁ - y₂)² )
Section Formula
- The section formula finds the coordinates of a point dividing a line segment in a given ratio.
- The coordinates of point P(x, y) dividing the line segment joining A(x₁, y₁) and B(x₂, y₂) internally in the ratio m₁:m₂ are: ( (m₁x₂ + m₂x₁) / (m₁ + m₂), (m₁y₂ + m₂y₁) / (m₁ + m₂) )
- When m₁ = m₂ (a 1:1 ratio), the point is the midpoint of the line segment.
- The midpoint of the line segment joining the points P(x₁, y₁) and Q(x₂, y₂) is: ( (x₁ + x₂) / 2, (y₁ + y₂) / 2 )
Applications
- The concepts of distance formula and section formula are used to identify geometrical figures.
- For instance, proving that four given points form a square, rectangle, or parallelogram can be achieved using these formulas.
- The formulas can also be used to determine the ratio in which a point divides a line segment or to find the coordinates of a point that divides a line segment in a particular ratio.
- Coordinate geometry is also used to solve problems related to area, perimeter, and other properties of geometrical figures.
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Description
This quiz covers fundamental concepts in coordinate geometry, including the distance formula and the section formula. You'll learn how to calculate distances between points and find coordinates of points dividing line segments. Test your understanding of how algebra applies to geometrical figures.
