SOLUTION: 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 coord

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): You can put this solution on YOUR website!

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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