Coordinates geometry concept explain with figure and example
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Coordinate geometry is a powerful branch of mathematics that bridges algebra and geometry. It uses a coordinate system to represent geometric shapes with numbers and equations, allowing us to solve geometric problems using algebraic methods. The foundation is the coordinate plane with X and Y axes intersecting at the origin.
The coordinate plane is formed by two perpendicular number lines. The horizontal line is called the X-axis, and the vertical line is called the Y-axis. These axes intersect at a point called the origin, with coordinates zero comma zero. The axes divide the plane into four regions called quadrants, numbered one through four in counterclockwise order.
Every point in the coordinate plane can be identified by an ordered pair of numbers called coordinates, written as x comma y. The x-coordinate tells us the horizontal distance from the Y-axis, while the y-coordinate tells us the vertical distance from the X-axis. For example, to plot point A at coordinates three comma two, we start at the origin, move three units to the right, then two units up.
Coordinate geometry allows us to calculate distances between points using the distance formula. The distance between two points with coordinates x one y one and x two y two is the square root of x two minus x one squared plus y two minus y one squared. For example, to find the distance between A at one comma one and B at four comma five, we substitute into the formula to get the square root of nine plus sixteen, which equals five units.
To summarize what we have learned about coordinate geometry: It is a powerful mathematical tool that combines algebra and geometry using a coordinate system. Points are represented by ordered pairs showing their position on the plane. The coordinate plane is divided into four quadrants by perpendicular axes. We can use formulas like the distance formula to solve geometric problems algebraically, making complex calculations much more manageable.