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

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) (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
The slope of is +1
A line perpendicular to it will have slope = -1

It goes through (2,4)

is the equation of AD
Find intersection of and
add the equations

also
(3,3) is the point D
To get the area of the square, find length AD and square it

note that is the area

area abcd
Answer by venugopalramana(3286) (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.

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