Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Three Vertices of a Parallelogram, Taken in Order, Are (−1, −6), (2, −5) and (7, 2). Write the Coordinates of Its Fourth Vertex. - Mathematics

Sum

Three vertices of a parallelogram, taken in order, are (−1, −6), (2, −5) and (7, 2). Write the coordinates of its fourth vertex.

#### Solution

Let $A\left( - 1, - 6 \right), B\left( 2, - 5 \right)\text{ and }C\left( 7, 2 \right)$ be the vertices of the parallelogram ABCD.
Let the coordinates of D be (x, y).
Since, diagonals of a parallelogram bisect each other,
$\frac{- 1 + 7}{2} = \frac{2 + x}{2}\text{ and }\frac{- 6 + 2}{2} = \frac{- 5 + y}{2}$
$\Rightarrow x = 4\text{ and }y = 1$"
Hence, the coordinates of the fourth vertex D are (4, 1).

Concept: Brief Review of Cartesian System of Rectanglar Co-ordinates
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 22 Brief review of cartesian system of rectangular co-ordinates
Q 4 | Page 21