Astraight line through points p and q is drawn perpendicular to a line through points p(x, y) and r(x,(y+10)) . the possible coordinates of the point q are_?

On the X-Y plane, the points p and r are on the vertical line X=x. Then the perpendicular (horizontal) line through p will have the equation Y=y. Points q on that line will have coordinates

... q(<anything>, y)

  or  

sin y = 7/q

7 is the opposite side length, q is the hypotenuse

tan y = 7/r

7 is the opposite side length, r is the adjacent side length

using sohcahtoa ^^^^

cos y = adjacent/hypotenuse

cos y = r/q