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mixed questions (need help) - HSN forum

# mixed questions (need help)

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### #1Dscott24

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Posted 12 March 2006 - 01:13 PM

Hi,

1. Two sides of a rectangle have equations y=2x and 2y+x=5. Find, algebraically, the coordinates of the vertex of the rectangle formed by these sides.

DScott24

### #2Steve

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Posted 12 March 2006 - 01:17 PM

Make a sketch of what's going on. Do you know what the question is actually asking you?
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### #3Dscott24

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Posted 12 March 2006 - 01:21 PM

QUOTE(Steve @ Mar 12 2006, 01:17 PM)

Make a sketch of what's going on. Do you know what the question is actually asking you?

I think i do, is it just the point where the two sides of the rectangle meet. Can you give me a hint on what im supposed to do?

DScott24

### #4Steve

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Posted 12 March 2006 - 01:31 PM

Well, if the lines intersect then you are looking for a point which lies on both the lines, i.e. solving the equation of the lines simultaneously.

Have a look at the new Straight Lines notes for more information.
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### #5Dscott24

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Posted 12 March 2006 - 01:43 PM

QUOTE(Steve @ Mar 12 2006, 01:31 PM)

Well, if the lines intersect then you are looking for a point which lies on both the lines, i.e. solving the equation of the lines simultaneously.

Have a look at the new Straight Lines notes for more information.

Yeah i just tried that, although i didnt get the right answer. can you try it and tell me what u got?

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### #6Steve

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Posted 12 March 2006 - 01:48 PM

I got (1,2).
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### #7Dscott24

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Posted 12 March 2006 - 01:50 PM

QUOTE(Steve @ Mar 12 2006, 01:48 PM)

I got (1,2).

Yeah thats the right answer, can you show me how you did it?

DScott24

### #8Steve

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Posted 12 March 2006 - 01:58 PM

Ok, you have:

So all you have to do is solve them simultaneously. There are lots of ways you can do this (all covered in the notes), but I did this:

From (1), (by multiplying through by 2), then substitute this into (2):

Then substitute this into either (1) or (2) to get the y-coordinate.
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