help with maths question (1 Viewer)

[AmieLea]

where A(-2,1); B(0,2); C(1,0) find D, such that ABCD is a square.

in the solutions it only shows us the graphical method, though i'm sure there's a way to answer it through equations and good old fashioned maths

(by the way, yes this should be a 2unit question, but i figure i'd have more chance of getting an answer through the 3unit forum lol.)

 

[pwoh]

Perpendicular gradients + distance formula for equal sides

 

[bouncing]

where A(-2,1); B(0,2); C(1,0) find D, such that ABCD is a square.

in the solutions it only shows us the graphical method, though i'm sure there's a way to answer it through equations and good old fashioned maths

(by the way, yes this should be a 2unit question, but i figure i'd have more chance of getting an answer through the 3unit forum lol.)

yep haha, i think this is year 11 stuff right?
all you need to do is find the gradients of AB, AC, AD, BD
if ABCD indeed is a square mAB=mCD and mBC=mAD
where mABxmBC=-1 (since its a right angle - perpendicular)

and then you can use distance formula for AB, BC, CD, AD - should all be the same cos thats a property only for a SQUARE