Coordinate Geometry and Linear Equations Quiz

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Questions and Answers

What is the general form of a linear equation in two variables?

  • $ax + by + c = 0$ (correct)
  • $ax + by = c$
  • $x + y + c = 0$
  • $x^2 + y^2 = c$

Which of the following describes the graph of every linear equation in two variables?

  • A straight line (correct)
  • A curve
  • A circle
  • A parabola

In coordinate geometry, what does the term 'abscissa' refer to?

  • The origin point
  • The vertical coordinate
  • The distance from the origin
  • The horizontal coordinate (correct)

Which identity represents the expansion of the squared difference of two variables?

<p>$(x-y)^2 = x^2 - 2xy + y^2$ (B)</p> Signup and view all the answers

What does the term 'Cartesian' refer to in geometry?

<p>A system to define points using coordinates (D)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

Flashcards

Horizontal Line

A horizontal line is a straight line extending infinitely in both directions that runs parallel to the x-axis on a coordinate plane.

Vertical Line

A vertical line is a straight line extending infinitely in both directions that runs parallel to the y-axis on a coordinate plane.

What is the origin?

The origin is the point where the x-axis and y-axis intersect on a coordinate plane. It has coordinates (0, 0).

What is an abscissa?

An abscissa is the x-coordinate of a point on a coordinate plane.

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What is an ordinate?

An ordinate is the y-coordinate of a point on a coordinate plane.

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Study Notes

Coordinate Geometry

  • Chapter 3 covers coordinate geometry
  • Key formulas include:
    • (x + y)² = x² + 2xy + y²
    • (x - y)² = x² - 2xy + y²
    • (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2xz
  • Key terms for understanding coordinate graphs include:
    • Horizontal axis
    • Vertical axis
    • Cartesian system
    • Coordinates
    • Quadrants
    • Origin
    • Abscissa
    • Ordinate
  • Chapter 3 is a prerequisite for understanding linear and other equations in two variables

Linear Equations in Two Variables

  • Chapter 4 details equations in two variables
  • General form of a linear equation is ax + by + c = 0
  • Graph of any such equation produces a straight line
  • The graph of a linear equation in two variables is always a straight line

Euclidean Geometry

  • Chapter 5 introduces Euclid's postulates and axioms
  • Euclid's geometry studies points, lines, and planes
  • Concepts covered in Chapter 5 are points, lines, axioms

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