f.4 a.maths

let m be x-coord of the required point

y = 2x - 3
point on the line, y-coord = 2m - 3
so, (m,2m - 3) is on y = 2x - 3

distance
= ! 3m + 2m - 3 - 2 ! / sqrt(10)
= ! 5m - 5 ! / sqrt(10)
= sqrt(10)

so, ! m - 1 ! = 2
m - 1 = 2 or m - 1 = -2
m = 3 or m = -1

(3,3), (-1,-5) are required points