Question

0. Three vertices of a parallelogram ABCD are (−2, 3), (6, 7) and (8,3). Find the fourth vertex D.

Answer 1

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Answer 2

Answer:

Coordinates of fourth vertex is D(0,-1)

Step-by-step explanation:

Given three of vertices of a parallelogram are A(-2,3), B(6,7), C (8,3).

we have to find the fourth vertex of parallelogram.

Let the coordinates of fourth vertex be D(x, y)

As the diagonals of parallelogram bisect each other

Hence midpoint of BD = midpoint of AC

By mid-point formula

$\text{Midpoint of line segment joining the points }(x_1,y_1)\text{ and }(x_2,y_2)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Midpoint of BD = Midpoint of AC

⇒ $(\frac{6+x}{2},\frac{7+y}{2})=(\frac{-2+8}{2}, \frac{3+3}{2})$

⇒ $(\frac{6+x}{2},\frac{7+y}{2})=(3,3)$

Comparing both sides

$\frac{6+x}{2}=3$  and    $\frac{7+y}{2}=3$

gives $x=6-6=0$    and   $y=6-7=-1$

Hence, coordinates of fourth vertex is D(0,-1)