Finding vertices C and D of a square with A(1,2) and B(2,4)

[Julian102]

Homework Statement

If two vertex of a square of the side AB is A(1,2) and B(2,4) find other two vertex C and D?

Homework Equations

1. y-y1 = m ( x-x1)
2. m=y1-y2 / x1-x2
3. m1*m2= -1
4. (x-x1) / (x1-x2) =(y-y1)/(y1-y2)
5. m=tanA
6. If ax+by+c=0 then its parallel line is ax+by+k=0

The Attempt at a Solution

Equation of AB is can be found using formula 4 , then slope is found using formula 2 . Then slope of perpendicular is -1/m (formula 3) . Now perpendicular AD and BC can be found using formula 1 . Now CD is parallel to AB . I need to find CD ...The distance between AB and CD is root 5 (of course since distance between AB is root 5 and it is a square) ...Please tell me how to find the side CD ...and diagonals AC and BD ...

 

[Samy_A]

Homework Statement

If two vertex of a square of the side AB is A(1,2) and B(2,4) find other two vertex C and D?

Homework Equations

1. y-y1 = m ( x-x1)
2. m=y1-y2 / x1-x2
3. m1*m2= -1
4. (x-x1) / (x1-x2) =(y-y1)/(y1-y2)
5. m=tanA
6. If ax+by+c=0 then its parallel line is ax+by+k=0

The Attempt at a Solution

Equation of AB is can be found using formula 4 , then slope is found using formula 2 . Then slope of perpendicular is -1/m (formula 3) . Now perpendicular AD and BC can be found using formula 1 . Now CD is parallel to AB . I need to find CD ...The distance between AB and CD is root 5 (of course since distance between AB is root 5 and it is a square) ...Please tell me how to find the side CD ...and diagonals AC and BD ...

Compute the equation of the line AB.
You can then easily write down the equations of the lines AD and BC (you gave the correct rules).
Then you can locate C and D (two possible solutions) on these lines using the distance.

Said differently: don't use words to describe a possible solution, just compute what you said.

 

[LCKurtz]

Alternatively, if you have studied vectors you don't need to deal with equations of straight lines and their slopes. Start with $\vec{AB} = \langle 1,2\rangle$. Can you write down a perpendicular vector of the same length? That would get you started.