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Sagot :
Given:
ABCD is a parallelogram, A(-3,-1), B(1,4), C(4,-1).
To find:
The x-coordinate of point D.
Solution:
Let the point D be (x,y).
We know that the diagonals of a parallelogram bisect each other. So, third midpoints are same.
Midpoint formula:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
In parallelogram ABCD, AC and BD are two diagonals.
Midpoint of AC = Midpoint of BD
[tex]\left(\dfrac{-3+4}{2},\dfrac{-1+(-1)}{2}\right)=\left(\dfrac{1+x}{2},\dfrac{4+y}{2}\right)[/tex]
[tex]\left(\dfrac{1}{2},\dfrac{-2}{2}\right)=\left(\dfrac{1+x}{2},\dfrac{4+y}{2}\right)[/tex]
[tex]\left(\dfrac{1}{2},-1\right)=\left(\dfrac{1+x}{2},\dfrac{4+y}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{1}{2}=\dfrac{1+x}{2}[/tex]
[tex]1=1+x[/tex]
[tex]1-1=x[/tex]
[tex]0=x[/tex]
Similarly,
[tex]-1=\dfrac{4+y}{2}[/tex]
[tex]-2=4+y[/tex]
[tex]-2-4=y[/tex]
[tex]-6=y[/tex]
The coordinates of point D are (0,-6).
Therefore, the x-coordinate of point D is 0.
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