SOLUTION: ABCD is a square. Point A has co-ordinates (2,4) and the line ODC has equation y=x. find the equation of line AD find the co-ordinates of point D find the area of square ABCD

Algebra ->  Triangles -> SOLUTION: ABCD is a square. Point A has co-ordinates (2,4) and the line ODC has equation y=x. find the equation of line AD find the co-ordinates of point D find the area of square ABCD      Log On


   

Question 61685: ABCD is a square. Point A has co-ordinates (2,4) and the line ODC has equation y=x.
find the equation of line AD
find the co-ordinates of point D
find the area of square ABCD
Found 2 solutions by josmiceli, venugopalramana:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equation of the line through (2,4) which is perpendicular
to the line y+=+x
The slope of y+=+x is +1
A line perpendicular to it will have slope = -1
y+=+mx+%2B+b
y+=+-x+%2B+b
It goes through (2,4)
4+=+-2+%2B+b
b+=+6
y+=+-x+%2B+6 is the equation of AD
Find intersection of y+=+x and y+=+-x+%2B+6
add the equations
2y+=+6
y+=+3
x+=+3 also
(3,3) is the point D
To get the area of the square, find length AD and square it
%28x%5Ba%5D+-+x%5Bd%5D%29%5E2+%2B+%28y%5Ba%5D+-+y%5Bd%5D%29%5E2++=+l%5E2
note that l%5E2 is the area
%282+-+3%29%5E2+%2B+%284+-+3%29%5E2+=+A
%28-1%29%5E2+%2B+1%5E2+=+A
A+=+1+%2B+1
A+=+2 area abcd

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
ABCD is a square. Point A has co-ordinates (2,4) and the line ODC has equation y=x.
find the equation of line AD
find the co-ordinates of point D
find the area of square ABCD
AD IS PERPENDICULAR TO ODC .HENCE ITS SLOPE IS -1
ITS EQN.IS
Y-4 = -1(X-2)
Y+X=6....IS THE EQN.OF AD.
SINCE D IS ON Y=X,ITS COORDINATES WILL BE (H,H) SAY
BUT IT IS ALSO ON AD .
HENCE IT WILL SATISFY EQN OF AD ..Y+X=6
H+H=6....H=3
COORDINATES OF D ARE (3,3)
SIDE OF SQUARE = AD = SQRT[(3-2)^2+(3-4)^2]=SQRT(2)
AREA OF SQUARE = [SQRT(2)]^2= 2 SQ.UNITS.