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1. C1:straight lines
Hi everyone,

I know this is one of the basic chapters, but I've got a question here:

ABCD is a rectangle in which the coordinates of A and C are (0,4) and (11,1) respectively, and the gradient of the side AB is -5.
a)find the equations of side AB and BC. OK, so I've got AB, y=-5x+4. But for BC, am I supposed to assume it's perpendicular to AB? The coordinates of B are given in the next step of the question, so do I need the information for this or is it possible to work out BC without the coordinates of B?
b)Show the coordinates of B is (1,-1)
c)Calculate the area of the rectangle.
Find the coordinates of the point on the y-axis which is equidistant from points A and D.
2. Re: C1:straight lines
a)It's a rectangle ABCD hence AB and CD are parallel and BC and DA are parallel. AB and CD must also be perpendicular to BC and DA. You have the coordinates of C, you only need one coordinate of the line to find the equation.

b) many ways of doing this, my preference would be to note that B is where both line BC and AB intersect.

c) relatively straight forward here however if you have any problems with it just ask
3. Re: C1:straight lines
OK thanks roar I'll get into it
4. Re: C1:straight lines
OK, so did b) fine, thanks

C) I just thought would be base x hight (AB = AC). So I used Pythagorus to do that. So forAB :

for AC:

Which totals

but the answer is 52! What did I do wrong?
Last edited by gavinlee; 11-05-2012 at 11:06.
5. Re: C1:straight lines
(Original post by gavinlee)
OK, so did b) fine, thanks

C) I just thought would be base x hight (AB = AC). So I used Pythagorus to do that. So forAB :

for AC:

Which totals

but the answer is 52! What did I do wrong?
AC isn't the height, it's the diagonal line throught the rectangle, use BC for the height.
6. Re: C1:straight lines
Thanks Roar, got that now.

For:
"Find the coordinates of the point on the y-axis which is equidistant from points A and D".

Is this just the y coordinate of the midpoint of line AD?
7. Re: C1:straight lines
(Original post by gavinlee)
Thanks Roar, got that now.

For:
"Find the coordinates of the point on the y-axis which is equidistant from points A and D".

Is this just the y coordinate of the midpoint of line AD?
Sorry was away. That won't be the answer since AD does not lie on the y axis.

A point on the y axis has the equation (0,y)

distance from A to this point = ((0-0)2 + (4-y)2)1/2

You can do the same with B and use simultaneous equations to find y when distance from A to this point=distance from B to this point.
Last edited by roar558; 11-05-2012 at 13:24.
8. Re: C1:straight lines
Hi Roar - thanks for your reply. But wouldn't what you suggested give us the point equidistant from A and from B, when the question asks for equidistance from A and D?
9. Re: C1:straight lines
(Original post by gavinlee)
Hi Roar - thanks for your reply. But wouldn't what you suggested give us the point equidistant from A and from B, when the question asks for equidistance from A and D?
sorry was a typo meant do the same with D it's the same principles though A and D aren't both on the y axis.
10. Re: C1:straight lines
(Original post by roar558)
sorry was a typo meant do the same with D it's the same principles though A and D aren't both on the y axis.
OK thanks very much for your help today