Answer:
The required point is, (7, -2)
Step-by-step explanation:
The straight line passing through (0,0) and (2,7) is,
y = ![(\frac {7 -0}{2-0}) \times x](https://tex.z-dn.net/?f=%28%5Cfrac%20%7B7%20-0%7D%7B2-0%7D%29%20%5Ctimes%20x)
⇒ y = 3.5x --------------(1)
Now, the straight line perpendicular to this line and passing through (0, 0) is
y = ![(\frac {-1}{3.5}) \times x](https://tex.z-dn.net/?f=%28%5Cfrac%20%7B-1%7D%7B3.5%7D%29%20%5Ctimes%20x)
⇒ 7y + 2x = 0 -------------(2)
Let, (h,k) be the required point.
then, it is on the line 7y + 2x = 0
⇒7k + 2h = 0
⇒k =
------------(3)
Again, distance from (0,0) of (h, k) is same as that of (2,7)
⇒ ![h^{2} + k^{2} = 4 + 49 = 53](https://tex.z-dn.net/?f=h%5E%7B2%7D%20%2B%20k%5E%7B2%7D%20%3D%204%20%2B%2049%20%3D%2053)
⇒
= 53 [putting the value of k from (3)]
⇒
= 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)