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Can someone help me with this, If in a parallelogram ABDC, the coordinates of A,B and C are respectively (1,2), (3,4) and (2,5) , then the equation of the diagonal AD is:

If in a parallelogram ABDC, the coordinates of A,B and C are respectively (1,2), (3,4) and (2,5) , then the equation of the diagonal AD is:

  • Option 1)

    5x-3y+1=0

  • Option 2)

    3x-5y+1=0

  • Option 3)

    5x+3y-11=0

  • Option 4)

    3x+5y-13=0

Answers (1)
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Mid-point formula -

x= \frac{x_{1}+x_{2}}{2}

y= \frac{y_{1}+y_{2}}{2}

 

- wherein

If the point P(x,y) is the mid point of line joining A(x1,y1) and B(x2,y2) .

 

 

Two – point form of a straight line -

y-y_{1}=\left ( \frac{y_{2}-y_{1}}{x_{2}-x_{1}} \right )(x-x_{1})

 

- wherein

The lines passes through  (x_{1}y_{1})  and  (x_{2}\, y_{2})

 

As BD and AC are parallel

\frac{n-4}{m-3}=\frac{5-2}{2-1}

{n-4}=3({m-3})..............................(1)

As AB and CD are parallel

\frac{n-5}{m-2}=\frac{4-2}{3-1}=\frac{2}{2}=1

{n-5}=({m-2})..............................(2)

Solving (1) and (2)

m=4 and n=7

\vec{DA} \: \: is\: \: (y-2)=(\frac{7-2}{4-1})(x-1)

             =>5x-3y+1=0


Option 1)

5x-3y+1=0

Option 2)

3x-5y+1=0

Option 3)

5x+3y-11=0

Option 4)

3x+5y-13=0

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