Two points A and B are given.Find the set of feet of the perpendiculars dropped from the point A onto all possible straight lines passing through the point B
To find the set of feet of the perpendiculars dropped from point A onto all possible straight lines passing through point B, we can follow these steps:
1. Coordinate System: Assign coordinates to points A and B on a coordinate system. Let's say A is (x1, y1) and B is (x2, y2).
2. Equation of Line: Find the equation of the straight line passing through point B. We know that the equation of a straight line passing through points (x1, y1) and (x2, y2) is given by the formula:
(y - y2) = m(x - x2)
where m is the slope of the line.
To find the slope m, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values, we can find the equation of the line passing through point B.
3. Perpendicular Foot: Now, for each line passing through B, we can find the foot of the perpendicular from point A onto the line. To find the foot, we need to find the intersection point of the line passing through B and the line perpendicular to it from point A.
Suppose the equation of the line passing through B is y = mx + c. The slope of the perpendicular line is -1/m.
We also know that the foot of the perpendicular lies on both lines. By substituting the values of x and y from the equations of both lines, we can solve for the values of x and y.
4. Repeat Step 3: Repeat step 3 for all possible lines passing through point B. Each time, you will find the foot of the perpendicular from point A onto a line.
5. Set of Feet: The set of feet of the perpendiculars dropped from point A onto all possible straight lines passing through point B is the set of all coordinates (x, y) that you obtained in step 4.
By following these steps, you can find the set of feet of the perpendiculars dropped from point A onto all possible straight lines passing through point B.