hello forum.

i'm studying maths as level on my own from text books and i'm getting stuck fairly often

please help me !!!

i'm stuck on part (d) of this question.

(a) find the equation of the line L through the point A(2,3) with gradient -1/2

answer = 2y = x +2

(b) show that the point P with coordinates (2 + 2t, 3 - t) will always lie on on L whatever the value of t.

which i can do.( although i would be unsure how to word the answer in an exam).

(c) find the values of t such that the length AP is 5 units.

answer = √5 and -√5

now for...

(d) find the value of t such that OP is perpendicular ( where O is the origin ).Hence find the length of the perpendicular from O to L.

answer = the value of t is -1/5 but i have no idea how to calculate the length of O to L (OP).

can anyone walk me through it?