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 ??
