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Coordinate geometry, or analytic geometry, uses a Cartesian coordinate system to analyze geometric figures algebraically. It covers linear equations, graphing straight lines, circle equations, and parametric equations for describing curves and motion. This field is crucial in physics, engineering, and computer graphics for spatial analysis.
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Coordinate geometry is a mathematical discipline that uses a coordinate system to precisely analyze geometric figures
Analytic geometry is another name for coordinate geometry
The purpose of coordinate geometry is to represent geometric entities algebraically and perform calculations to determine distances, midpoints, slopes, and equations of lines and curves
The Cartesian coordinate system is defined by two perpendicular number lines, the x-axis (horizontal) and the y-axis (vertical)
x-axis
The x-axis is the horizontal number line in the Cartesian coordinate system
y-axis
The y-axis is the vertical number line in the Cartesian coordinate system
Origin
The origin is the point where the x-axis and y-axis intersect, dividing the plane into four quadrants
Linear equations are algebraic expressions that form the basis of coordinate geometry and are represented graphically by straight lines on the Cartesian plane
The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept
Slope
The slope of a line measures its steepness and direction, with positive slopes indicating an upward tilt and negative slopes a downward tilt
Y-intercept
The y-intercept is the point where the line crosses the y-axis
Parallel and Perpendicular Lines
The concept of slope is instrumental in determining whether lines are parallel (having equal slopes) or perpendicular (having slopes that are negative reciprocals of each other)
A circle is a fundamental shape in coordinate geometry, defined as a set of points equidistant from a central point
The standard equation for a circle in the Cartesian plane is (x-h)^2 + (y-k)^2 = r^2, where (h, k) is the center of the circle and r is its radius
Pythagorean Theorem
The equation for a circle is derived from the Pythagorean theorem
Tangency
A tangent to a circle is a line that intersects the circle at exactly one point and is perpendicular to the radius at that point
Equation of a Tangent Line
The equation of a tangent line can be found using the point of tangency and the slope, which is the negative reciprocal of the slope of the radius at that point
00
______ geometry, also known as ______ geometry, uses a coordinate system to analyze geometric figures.
Coordinate
analytic
01
General form of a linear equation
y = mx + b, where 'm' is slope, 'b' is y-intercept.
02
Interpretation of slope value
Positive slope: line tilts up. Negative slope: line tilts down.
