Question 1123947: ABCD is a rectangle/ The coordinates of A and B are (1,4) and (5,2) respsectively. The x-coordinate of D is -2. Find:
a) the equation of AD
b) the y-coordinate of D
c) the coordinates of C
Answer by MathLover1(20855)   (Show Source):
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 is a rectangle
The coordinates of  and  are ( , ) and ( , ) respectively.
The x-coordinate of  is  . -> is at (, )
Find:
a) the equation of 
we will first find a slope of line that contais , a line that is perpendicular to the line that contains :
use given points (,) and (,) to find slope 
 will have a slope  ...use given point that lie on AB (,) (
and, your equation o the line {{AD}}} is: 
b) the y-coordinate of
to find it, use  and (,)
so, is at (,)
c) the coordinates of 
point is intersection point o the line  and 
since the line is parallel to the line , they have same slope
equation of the line is:
 ....use point which is at (,)
 .....eq.1
and equation of has a slope  and is parallel to
so,equation of the line is:
 ....use point which is at (,)
and  .....eq.2
from eq.1 and eq.2 we have
go to .....eq.2, plug in 
so, point is at (, )
(,) and (,)
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