Question

The straight line p passes through the point (10,1) and is perpendicular to the line r with equation 2x+ y = 1. Find the equation of p. Find also the coordinates of the point of intersection of p and r, and deduce the perpendicular distance from the point (10,1) to the line r.

Answer 1

the required line is y=1/2x+c. since it is perpendicular the given line. By substituting the P(10,1) in the equation, you get the value of c= -4. The line is x-2y=8(after rearranging). now solving these 2 equations as simultaneous equations. we get the point of intersection as (2,-3). And the distance from distance formula will give us the length of perpendicular as \[\sqrt{80}\]