Objectives:
1. To determine the position of a point in a plane we draw to mutually perpendicular straight lines XOX’ and XOX’.
2. To realize the need o having an embedding structure ( a metric ) to be able to measure distance.
3. To find the slope of a line given two points.
4. Determine whether two lines are parallel or perpendicular.
5. Find the equation of a straight line, given two points lying on it;
Analytical Geometry
Analytical Geometry is a combination of algebra and geometry. In analytical geometry, we aim at presenting the geometric figures using algebraic equations in a two-dimensional coordinate system or in a three-dimensional space. Analytical geometry includes the basic formulas of coordinate geometry, equations of a line and curves, translation and rotation of axes, and three-dimensional geometry concepts.
Let us understand the various sub-branches of analytical geometry, and also check the examples and faqs on analytical geometry.
What Is Analytical Geometry?
Analytical geometry is an important branch of math, which helps in presenting the geometric figures in a two-dimensional plane and to learn the properties of these figures. Here we shall try to know about the coordinate plane and the coordinates of a point, to gain an initial understanding of Analytical geometry.
A cartesian plane divides the plane space into two dimensions and is useful to easily locate the points. It is also referred to as the coordinate plane. The two axes of the coordinate plane are the horizontal x-axis and the vertical y-axis. These coordinate axes divide the plane into four quadrants, and the point of intersection of these axes is the origin (0, 0). Further, any point in the coordinate plane is referred to by a point (x, y), where the x value is the position of the point with reference to the x-axis, and the y value is the position of the point with reference to the y-axis.
The properties of the point represented in the four quadrants of the coordinate plane are:
· The origin O is the point of intersection of the x-axis and the y-axis and has the coordinates (0, 0).
· The x-axis to the right of the origin O is the positive x-axis and to the left of the origin, O is the negative x-axis. Also, the y-axis above the origin O is the positive y-axis, and below the origin O is the negative y-axis.
· The point represented in the first quadrant(x, y) has both positive values and is plotted with reference to the positive x-axis and the positive y-axis.
· The point represented in the second quadrant is (-x, y) is plotted with reference to the negative x-axis and positive y-axis.
· The point represented in the third quadrant (-x, -y) is plotted with reference to the negative x-axis and negative y-axis
· The point represented in the fourth quadrant (x, -y) is plotted with represented in the positive x-axic and negative y-axis..