lazyjilo.blogg.se - Coordinate geometry proofs answer key

The distance between two points \((x_1, y_1)\) and \(x_2, y_2) \) is equal to the square root of the sum of the squares of the difference of the x coordinates and the y-coordinates of the two given points. Let us know more about each of the formulas in the below paragraphs. The formulas of coordinate geometry are the distance formula, slope formula, midpoint formula, section formula, and the equation of a line. The formulas of coordinate geometry help in conveniently proving the various properties of lines and figures represented in the coordinate axes. The coordinates of a point are useful to perform numerous operations of finding distance, midpoint, the slope of a line, equation of a line.

Ordinate: It is the y value in the point (x, y)., and is the perpendicular distance of the point from the x-axis, which is parallel to the y-axis.

Abscissa: It is the x value in the point (x, y), and is the distance of this point along the x-axis, from the origin.

The point represented in the fourth quadrant (x, -y) is plotted with reference to the positive x-axis and negative y-axis.Ī coordinate is an address, which helps to locate a point in space. For a two-dimensional space, the coordinates of a point are (x, y). Here let us take note of these two important terms.

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 second quadrant is (-x, y) is plotted with reference to the negative x-axis and positive 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.Also, the y-axis above the origin O is the positive y-axis, and below the origin O is the negative y-axis. 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.The origin O is the point of intersection of the x-axis and the y-axis and has the coordinates (0, 0).The properties of the point represented in the four quadrants of the coordinate plane are: 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.

These coordinate axes divide the plane into four quadrants, and the point of intersection of these axes is the origin (0, 0). The two axes of the coordinate plane are the horizontal x-axis and the vertical y-axis. Coordinate PlaneĪ 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. Here we shall try to know about the coordinate plane and the coordinates of a point, to gain an initial understanding of Coordinate geometry. Practice Questions on Coordinate GeometryĬoordinate 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. Figures such as straight lines, curves, circles, ellipse, hyperbola, polygons, can be easily drawn and presented to scale in the coordinate axes. Further coordinate geometry helps to work algebraically and study the properties of geometric figures with the help of the coordinate system. Similarly locating the point in a plane or a piece of paper, we have the coordinate axes with the horizontal x-axis and the vertical y-axis.Ĭoordinate geometry is the study of geometric figures by plotting them in the coordinate axes. The zero degrees 'Greenwich Longitude' and the zero degrees 'Equator Latitude' are the starting lines of this coordinate system. The coordinate system of our earth is made up of imaginary lines called latitudes and longitudes. Every place on this planet has coordinates that help us to locate it easily on the world map.