Math Is Fun Forum

naturewild

Member

Registered: 2005-12-04

Posts: 30

Geomtery Proof

Prove : The perpendicular distance from a point P(x1,y1) to the straight line whose equation is Ax + By + c = 0 is

d = absolute value (Ax1 + By1 + c)  / square root (A² + B²)

Also another problem not related to geometry is this :

When an integer is divided by 15, the remainder is 7. Find the remainders when the same integer is divided by 3 and 5.

Thanks in advance!

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,423

Re: Geomtery Proof

naturewild, I shall attempt the second problem first.
When an integer is divided by 15, the remainder is 7.
Therefore, the number is of the form 15n+7, where n is a certain Natural number. When 15n+7 is divided by 5, since 15n is divisible by 5, the remainder is what it would be when 7 is divided by 5, hence, the remainder is 2.When 15n+7 is divided by 3, since 15n is divisible by 3, the remainder is what it would be when 7 is divided by 3, hence the remainder is 1.

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naturewild

Member

Registered: 2005-12-04

Posts: 30

Re: Geomtery Proof

Thanks for the solution to the second problem. Your coloring makes it so easy to understand.
Thanks once again ^^

Actually I have one more problem I'm stuck with, but I'm satisfied with only these 2 solutions ^_^