1. problem: COORDINATES AND SURDS?

hello forum.

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

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.

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?

2. hello Miasmagasma,..
check your answer for question (a), the equation should be $2y=-x+8$.

for question (d), do you mean that OP is perpendicular to L?

it would be better if you write your answer in details for part (b) and (c) so we can check it.

3. Originally Posted by Miasmagasma
hello forum.

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

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
As Dedust suggested, this has slope 1/2, not -1/2.

(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).
Once you have the correct equation, just put x= 2+ 2t, y= 3- t into the equation and show that it is true no matter what t is.

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

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).
I think you should recheck (c) and (d) with the correct equation

can anyone walk me through it?
Once you have the correct value of t, put it into the given equations to find x and y. Then use the formula $\sqrt{(x_1- x_0)^2+ (y_1-y_0)^2}$ to find the length.