Fınding the position of a point on the line

In summary, the conversation discusses finding the coordinates of a point Q on a perpendicular line from point P to line l_1. The speaker is looking for a single equation that can describe the coordinates of point Q, and suggests using one of the methods mentioned to find an expression for Q in terms of P and l_1.
  • #1
Arman777
Insights Author
Gold Member
2,168
193
Let us suppose we have a line ##l_1 = ax + by + c = 0## and we have a point P, ##P(x_p, y_p)## that is outside of this line. If we draw a perpendicular line from point ##P## to a point on the ##l_1##. What would be the coordinates of this point ? I know there are many ways to do it. But I am looking for a single equation that can describe this point (##Q##) ?

1565105884095.png
 
Mathematics news on Phys.org
  • #2
Have you considered using one of those methods to solve the problem, which should give you an expression for [itex]Q[/itex] in terms of [itex]P[/itex] and [itex]l_1[/itex]?
 
  • Like
Likes Vanadium 50 and Mark44

FAQ: Fınding the position of a point on the line

What is the process for finding the position of a point on a line?

The process for finding the position of a point on a line involves determining the coordinates of the point and using the slope of the line to calculate the distance from the point to the origin.

What is the formula for finding the position of a point on a line?

The formula for finding the position of a point on a line is y = mx + b, where m is the slope of the line and b is the y-intercept.

How is the slope of a line used to find the position of a point?

The slope of a line is used to find the position of a point by determining the ratio of the change in y-coordinates to the change in x-coordinates between two points on the line. This ratio represents the rate at which the line is increasing or decreasing.

Can the position of a point on a line be negative?

Yes, the position of a point on a line can be negative. This occurs when the point is located below the x-axis, resulting in a negative y-coordinate.

What other factors besides the slope of a line can affect the position of a point?

Other factors that can affect the position of a point on a line include the y-intercept, the direction of the line (positive or negative slope), and the distance of the point from the origin.

Similar threads

I Prove that the geometric mean is always the same
Replies
2
Views
1K
I On a proof of the converse of the supporting hyperplane theorem
Replies
9
Views
1K
B Existence of parallels in axiomatic plane geometries
2
Replies
36
Views
4K
I How can you represent a point by "z = x + iy" as shown here?
Replies
10
Views
2K
A check: shortest distance from point to line
Replies
2
Views
2K
MHB Parametric Eqs: Find Line & Plane, Find Triangle Area
Replies
4
Views
1K
B Invariant under rotation: Banal, obvious, or noteworthy?
Replies
2
Views
1K
I Expressing any given point on plane with one unique number
Replies
4
Views
1K
I Two vectors and two perpendicular lines
Replies
20
Views
1K
MHB Determining c in Quadratic Function Turning Point
Replies
6
Views
1K

Hot Threads

Recent Insights

Back
Top