Answer with explanation:
Property of Quadrilateral A B CD
⇒Equation of Line AD is, y= -3 x.
⇒Equation of Line BC is, y= -3 x +11
Coordinates of CD = C(2,5) and D(-1,3)
Equation of line CD will be
[tex]\frac{y-5}{x-2}=\frac{3-5}{-1-2}\\\\-3 \times (y-5)=-2\times (x-2)\\\\-3 y +15=-2 x +4\\\\2 x -3 y +11=0[/tex]
Equation of line AB will be, which is parallel to CD, as opposite sides of parallelogram are parallel and equal,is equal to
2 x -3 y + k=0
Because when lines are parallel their slopes are equal.
→→Equation of line AD is , y= - 3 x.
Coordinates of point A can be calculated by
→2 x -3 × (-3 x ) +k=0
→2 x +9 x +k=0
[tex]\rightarrow x=\frac{-k}{11}\\\\\rightarrow y=\frac{3k}{11}[/tex]
→→→Similarly, Coordinate of point D can be calculated by solving these two lines:
y = -3 x + 11
2 x -3 y + k=0
→2 x -3 × (-3 x +11) +k=0
→2 x +9 x -33 +k=0
→11 x =33 -k
[tex]x=\frac{33-k}{11}[/tex]
[tex]y=-3 \times \frac{33-k}{11}+11\\\\y=\frac{-99+3 k+121}{11}\\\\y=\frac{22+3 k}{11}[/tex]
→→Coordinates of A is [tex](\frac{-k}{11},\frac{3k}{11})[/tex]
Coordinates of Point D is [tex](\frac{33-k}{11},\frac{22+3k}{11})[/tex].
you, can get infinite number of ordered pairs, for different value of k.
For, k=0 ,
A= (0,0)
D=(3,2)
