Please help with this coordinate geometry question!

1) i) The straight line p is perpendicular to the line with equation x+2y=1 and passes through the point A (a,2). Find, in terms of the constant a, an equation for the line p.

1) ii) Given that the line p crosses the y-axis at the point B (0,3), find the value of a, and hence find the distance AB.

For part i) I found the gradient of line p to be 2 and came up with the final answer as 2x-y=-2(1-a), is this correct? As for part ii) I found a to be -1/2 but I can't proceed any further until I know that I'm getting the right answers.

Thanks for any help

Correct but a very untidy way of writing the equation

You will not be able to check partial answers in an exam

Sorry but what do you mean by untidy? I found the distance AB to be
sqr(5/4).

I mean untidy

Why not write it as y =

Why have that -2 on the right hand side



Correct for AB though I would square root the 4

So now I'm stuck on this question :/

Two straight lines have equations x+3y=13a and 3x-y=9a+10, where a is a constant. Their point of intersection is denoted by A.
Find, in terms of a, the coordinates of A.

How would I start as there are 3 variables!

Do as you would normally do

The third variable is a and will be in the answers

So I got (4a+3, 3a-1)?