Maths / Coordinate Geometry / Mid Point Formula

QUESTION

ABCD is a parallelogram with vertices $\dpi{120} \large \dpi{120} \large A(x_1,y_1),B(x_2,y_2)and \;C(x_3,y_3)$ Find the coordinates of the fourth vertex D in terms of $\dpi{120} \large x_1,x_2,x_3,y_1,y_2,y_3$

EXPLANATION
Explain TypeExplanation Content
Text

Let the coordinate of D be (x,y) We know that diagonals of a parallelogram bisect each other .

Angle required

Therefore mid-point of AC = mid -point of BD

$\dpi{120} \large \left ( \frac{x_1+x_3}{2},\frac{y_1+y_3}{2} \right )=\left ( \frac{x_2+x}{2},\frac{y_2+y}{2} \right )$

$i.e., x_1+x_3=x_2+x\: and\: \;y_1+y_3=y_2+y$

$i.e., x_1+x_3-x_2=x\;and\; y_1+y_3-y_2=y$

Thus, the coordinates of D are

$(x_1+x_3-x_2,y_1+y_3-y_2)$

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