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December 17th, 2009, 12:56 AM   #1
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Find points on a line of equal distance from certain point

Hi Gents,

We have line L1: 3 X + 4 Y + 12 = 0
I got the X-intercept (M) (-4,0)
Y-intercept (A) (0,-3)
Distance (d) between A and M (d=4)

Then I got line, L2, which is perpendiclar to L1 through M
L2: 3 Y = 4 X +16
Anyone can confirm answers?


THEN I STUCK ON:
- Finding 2 points B & C on L2 whose distance from A = d* sq. root of 2 (d ?2)
- Finding a point D that makes ABCD a square

Thanks alot
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December 17th, 2009, 08:23 AM   #2
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Re: Find points on a line of equal distance from certain point

Hi horees;

A) is correct

M) is correct

d is not correct, the distance between A and M is 5

L2 is correct.

The 2 points you want that are 5 sqrt(2) away from (0,-3) and on L2 are (-7,-4) and (-1,4)
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December 18th, 2009, 10:39 AM   #3
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Re: Find points on a line of equal distance from certain point

how u got (-7,-4) & (-1,4)???
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December 18th, 2009, 01:22 PM   #4
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Re: Find points on a line of equal distance from certain point

Hi horees;

I would be glad to. Here is how I did it. It is a little long and tedious. I will provide the overview and you can ask me for a further explanation if you want it.

Here is how I got the distance from A to M.



This is how I found the 2 points that are on L2 and that are 5 sqrt(2) away from (0,-3)



By squaring both sides the above equation becomes a quadratic with x = - 1 and x = - 7. Substituting for both x's into L2:





So the points are (-7,-4) and (-1, 4)
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