Answer:The required point is, (7, -2)Step-by-step explanation:The straight line passing through (0,0) and (2,7) is,y = [tex](\frac {7 -0}{2-0}) \times x[/tex]⇒ y = 3.5x --------------(1)Now, the straight line perpendicular to this line and passing through (0, 0) is y = [tex](\frac {-1}{3.5}) \times x[/tex]⇒ 7y + 2x = 0 -------------(2)Let, (h,k) be the required point.then, it is on the line 7y + 2x = 0⇒7k + 2h = 0 ⇒k = [tex](\frac {-2}{7}) \times h[/tex] ------------(3)Again, distance from (0,0) of (h, k) is same as that of (2,7)⇒ [tex]h^{2} + k^{2} = 4 + 49 = 53[/tex]⇒[tex]h^{2} \times (\frac {53}{49})[/tex] = 53 [putting the value of k from (3)]⇒[tex]h^{2}[/tex] = 49⇒h = 7 [since, (h,k) is in 4th quadrant, so,h >0]So, k = -2 [putting the value of h in (3)]So, the required point is, (7, -2)