Calculating Perpendicular Point on a Line in 2D Plane

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In summary, the conversation discusses the calculation of the point C which makes AC perpendicular to BC. The suggested method is to substitute v to C and equate the inner product of AC and BC to zero. However, without specific values, the equation cannot be simplified further.
  • #1
Asuralm
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Hi all:

Given a line L:v= v0+t*n; and two points A, B in 2D plane; A and B are on the two sides of the line L. I want to calculate the point C which makes AC is perpendicular to BC

I know it's simply that substitude v to C and <AC, BC>=0. But I don't know how to simplify the equation.

Could anyone help me please?

Thanks
 
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  • #2
Asuralm said:
Hi all:

Given a line L:v= v0+t*n; and two points A, B in 2D plane; A and B are on the two sides of the line L. I want to calculate the point C which makes AC is perpendicular to BC
C is on L?

I know it's simply that substitude v to C and <AC, BC>=0. But I don't know how to simplify the equation.

Could anyone help me please?

Thanks
The vector AC= v0+ t*n is given by v0+ t*n-A. The vector BC is given by v0+ t*n- B.
Their inner product <AC,BC>= <v0+ t*n- A,v0+ t*n- B>= |v0- t*n|2- <v0+ t*n,A+B>+ <A,B>.
Without specific values for A and B, v0 and n, I don't see how you can get any simpler than that.
 
  • #3
should this |v0- t*n|2- <v0+ t*n,A+B>+ <A,B>

be <v0+t*n, v0+t*n> - <v0+t*n, A+B> + <A, B> ?
 

1. How do I calculate a point in a Cartesian coordinate system?

In order to calculate a point in a Cartesian coordinate system, you will need to know the x and y coordinates of the point. First, plot the point on the coordinate plane using the x and y values. Then, use the Pythagorean theorem to find the distance of the point from the origin (0,0). Finally, use trigonometric functions to determine the angle of the point from the x-axis.

2. What is the formula for calculating a point's distance from the origin?

The formula for calculating a point's distance from the origin is d = √(x² + y²), where d represents the distance and x and y are the coordinates of the point on the Cartesian plane.

3. How do I find the angle of a point from the x-axis?

To find the angle of a point from the x-axis, you will need to use trigonometric functions such as sine, cosine, or tangent. The formula for calculating the angle is θ = tan⁻¹ (y/x), where θ is the angle and x and y are the coordinates of the point.

4. Can I use a calculator to find the coordinates of a point?

Yes, you can use a calculator to find the coordinates of a point. Most scientific calculators have functions for calculating distance and angles using the coordinates of a point. However, it is important to understand the formulas and concepts behind the calculations before relying on a calculator.

5. How do I calculate a point's coordinates on a 3D plane?

To calculate a point's coordinates on a 3D plane, you will need to use three values (x, y, z) instead of just two. Plot the point on the 3D coordinate system and use the distance formula and trigonometric functions to find the distance and angles of the point from the origin. In addition, you will also need to determine the point's height or z-value in relation to the xy-plane.

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