Rectangle ABCD

A is (-1,4), B is (4,8)

Equation of BC is 4y + 5x= 52

equation of AD is 4y + 5x = 11

equation of AB is 5y= 4x+ 24

Find C and D

Answer is (12,-2) and (7,-6)

I've tried gradient,length,midpoint formulas but to no avail.

Thanks

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- Aug 13th 2013, 02:23 AMRodimus79Finding 2 vertices of rectangle with 2 known vertices
Rectangle ABCD

A is (-1,4), B is (4,8)

Equation of BC is 4y + 5x= 52

equation of AD is 4y + 5x = 11

equation of AB is 5y= 4x+ 24

Find C and D

Answer is (12,-2) and (7,-6)

I've tried gradient,length,midpoint formulas but to no avail.

Thanks - Aug 13th 2013, 03:29 AMMarkFLRe: Finding 2 vertices of rectangle with 2 known vertices
The problem, as posed, has no unique solution. Is there some other attribute of the rectangle which you have not posted, such as its area?

- Aug 13th 2013, 05:18 AMRodimus79Re: Finding 2 vertices of rectangle with 2 known vertices
Apologies..I left out

Length of BC is twice the length Of AB - Aug 13th 2013, 06:11 AMHallsofIvyRe: Finding 2 vertices of rectangle with 2 known vertices
And, you now tell us, "Length of BC is twice the length Of AB"

It is easy to calculate that the length of AB is

so the length of BC is and, because this is a rectangle, BC and AD are the same length.

Take D= (x, y)= (x, (11- 5x)/4). Then we must have [tex]\sqrt{(x- (-1))^2+ ((11- 5x)/4- 4)^2}= 2\sqrt{41}[tex]

so that, squaring both sides gives . Solve that quadratic equation for x. Do the same with BC.

Quote:

Find C and D

Answer is (12,-2) and (7,-6)

I've tried gradient,length,midpoint formulas but to no avail.

Thanks

- Aug 13th 2013, 09:35 AMRodimus79Re: Finding 2 vertices of rectangle with 2 known vertices
Thanks so much, HallsofIvy!! The key step was to have y = 11-5x/4, to express y in terms of x, since it's a point on the line and satisifies the equation! Thanks once again!!!

- Aug 14th 2013, 07:58 PMibduttRe: Finding 2 vertices of rectangle with 2 known vertices
- Aug 16th 2013, 05:49 AMbjhopperRe: Finding 2 vertices of rectangle with 2 known vertices
given the two points and the fact that the length of the rectangle is twice width(AB) there is a simple method to find the other vertices

slope diagram AB = 4/5

slope diagram AD =-5/4

actual slope diagram AD =-10/8 since AD =2AC

Point D x =8-1 =7 y =4 + absolute value y =10 y=-6

same procedure gives point C - Aug 17th 2013, 01:41 AMibduttRe: Finding 2 vertices of rectangle with 2 known vertices
- Aug 17th 2013, 03:45 AMbjhopperRe: Finding 2 vertices of rectangle with 2 known vertices