The co-ordinates of the foot of the perpendicular from the point (2, 2) on the line y – 2x – 8 = 0 are (A) (–1, 6) (B) (–1, –4) (C) (–2, 10) (D) (2, 4) (E) (–2, 4)

Slope of the line y - 2x = 8 is 2. The slope the perpendicular drawn to it will be -(1/2). (because product of slopes of perpendicular lines is -1) Let's find the slope of the line with slope = -(1/2) and passing through (2,2) 2(y - 2) = -(x - 2) 2y + x = 6 The point of intersection of the two lines will be the foot of the perpendicular. Solving them, we get (x, y) = (-2,4) [spoiler](E)[/spoiler] is the answer

Looking for a better explanation

Slightly different approach. Dabral

Let me try(just try!) Equation of the line is y - 2x - 8 = 0. For the point (x1,y1) to be on the line y - 2x - 8 = 0, the value of (y1 -2*x1 - 8) should be equal to zero. i.e. y1 -2*x1 - 8 = 0 (A) (-1, 6) = y1 -2*x1 - 8 = 6 -(2*-1) - 8 = 8-8 = 0, Can be the answer (B) (-1, -4) = y1 -2*x1 - 8 = -4 -(2*-1) - 8 = -10 !=0, It is definitely not the answer (C) (-2, 10) = y1 -2*x1 - 8 = 10 -(2*-2) - 8 = 6 !=0, It is definitely not the answer (D) (2, 4) = y1 -2*x1 - 8 = 4 -(2*2) - 8 = -8!=0, It is definitely not the answer (E) (-2, 4) = = y1 -2*x1 - 8 = 4 -(2*-2) - 8 = 8-8 = 0, Can be the answer Now it is between A and E. Since, the slope of the line y - 2x - 8 is 2, the slope of the line perpendicular to the same line is -1/2. (A) Slope of line joining (2,2) and (-1,6) = 6-2/-1-2 = -4/3.It is definitely not the answer (E) Slope of line joining (2,2) and (-2,4) = 4-2/-2-2 = -1/2. Bingo ! So, answer choice E is the correct answer p.s: In my opinion, the solution by aneesh.kg(and Dabral) is a better and an easier one. p.p.s: Dabral : Do you use Wacom Bamboo for the drawings ??