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How do you determine if a point is above or below a line?
If the line equation is y=ax+b and the coordinates of a point is (x0,y0) then compare y0 and ax0+b, for example if y0>ax0+b then the point is above the line, etc.
What is direction numbers of a line?
Direction numbers: The numbers which are proportional to direction cosines of a line are called direction numbers of the line. Direction numbers of a line are not unique. Direction numbers of two parallel lines are the same. Normal vector to the plane ax + by + cz = d is a^i+b^j+c^k.
Which three points lie in the same line?
Three or more points that lie on the same line are collinear points . Example : The points A , B and C lie on the line m . They are collinear.
How to determine the side on which a point is on?
Let’s label the side n → points to + and the opposite side −. Then for any point ( x, y) in the plane, the sign of determines which side the point ( x, y) is on. Notice that this is 0 if and only if ( x, y) is on the line, so all points not on the line get + or −.
How to calculate which side of a line lies exactly?
If d = 0 then the point lies exactly line. To see whether points on the left side of the line are those with positive or negative values compute the value for d for a point you know is to the left of the line, such as ( x 1 − 1, y 1) and then compare the sign with the point you are interested in.
How to tell if a line is to the left or right?
If point’s x < line’s x, the point is to the left of the line. If point’s x == line’s x, the point is on the line. First check if you have a vertical line: Then, create an equation of the line using point slope form: y – y1 = m* (x-x1) + y1.
How to calculate which side of a line has a positive value?
To see whether points on the left side of the line are those with positive or negative values compute the value for $d$ for a point you know is to the left of the line, such as $(x_1-1,y_1)$ and then compare the sign with the point you are interested in.