| Solved by pluggable solver: Finding a distance between a point given by coordinates (x, y) and a line given by equation y=ax+b |
| We want to find the perpendicular distance between a point given by coordinates ( and a line given by equation First, let's draw a diagram of general situation with point P (xo, yo) and line L: y= a.x + b. The required distance is PC. (in the diagram below) Methodology We will first find the vertices of the triangle in order to get the side lengths and then by applying Sine Rule on right angle triangle PAB and PBC we will calculate the desired distance PC. Step1 Calculation of the vertices of triangle PAB: Draw a vertical line passing through the point 'P'. This line at point 'A'. The X coordinate of A(x1) will be same as 'A' we will use the fact that point 'A' lies on the given line 'L' and satisfies the equation of the line 'L' . Now, plug this Hence, Point (A)( Similarly, Draw a horizontal line passing through the point 'P'. This line at point 'B'. The Y coordinate of B(y2) will be same as B we will use the fact that point 'B' lies on the given line 'L' and satisfies the equation of the line 'L' . Now, plug this Hence, Point (B)( Now, we have all the vertices of the triangle PAB Step2 Calculation of the side lengths using distance formula: Hence, The side lengths PA, PB and AB are Step3 Apply Sine rule on common angle B in triangle PAB and triangle PBC. Both triangle PAB and triangle PBC are right angle triangle and points 'A', 'B' and 'C' lay on the given line L. PC is the required perpendicular distance of the point P (4, 2) from line given lineL1: y=0.75*x+-31. For better understanding of this concept, look at the Lesson based on the above concept. Lesson |