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The sum of two straight lines and equations is a compulsory course in senior two mathematics.
Let P(a, -a/2)

OP^2=a^2+a^2/4=5a^2/4

The distance from p to the straight line x+2y-3=0 d=la-a-3l/ root number (1+4)=3/ root number 5=3 root number 5 /5.

So the root number 5 a/2=3 and the root number 5/5.

a=6/5

P(6/5,-3/5)