Point can be defined as that geometrical mark that does not have any dimensions and is represented using coordinates in the Cartesian system. But still it has much importance in math geometry. For defining a plane we must have at least three collinear points. From one point as many circles and lines can pass but when two points are considered, only one line and infinite number of circles can pass. When the number of points becomes three, only one circle can pass through it. For a point to lie on any curve or geometrical figure, it must satisfy the equation of that curve or figure.
For a point we define locus and also write the equation that will be specific for many such points. So, if we are defining a locus we must have all such points which satisfy certain conditions.
Example: Suppose we have a line 5y = 8x – 3, then find whether the points (2, 4) and (1, 1) satisfy it or not?
Solution: For the points (2, 4) and (1, 1) to lie on the line 5y = 8x – 3, they must satisfy the given equation. So, substituting them in the equation we can check whether they lie on the line or not:
For (2, 4),
5 y = 8 x – 3,
5 * 4 = 8 * 2 – 3,
Or 20 = 13 which is not possible,
For (1, 1),
5 y = 8 x – 3,
5 * 1 = 8 * 1 – 3,
Or 5 = 5,
Thus 2nd point lies on the line.
For (2, 4),
5 y = 8 x – 3,
This is how we make use of point geometry by using the coordinates of points which can be either in the form of rectangular coordinates or polar coordinates.
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In math we have theorems based on various concepts that are actually possible to be proved. It is a kind of fact that is written in form of a statement. Likewise we have a suitable proof for the theorem that states if a Point Lies outside a line, then exactly one plane contains the line and point...Read More