Question

1. A(-1,0),B(3,1) and C(2,2) are the vertices of a parallelogram ABCD. The coordinates of the fourth

vertex D is

(a) (0,-3) (b) (6,3) (c) (0,3) (d) (-2,1)
​

Answer 1

Given:

The points A(-1,0), B(3,1), C(2,2)

To find:

The fourth vertex D of the parallelogram ABCD

Calculation:

Let the fourth vertex is D(x,y). In a parallelogram the diagonals bisect each other i,e., Midpoints of the diagonals are equal

In the parallelogram ABCD, AC and BD are two diaognals. Hence their midpoints are equal

$\Rightarrow Midpoint\ of \ AC \ = Midpoint \ of \ BD$

$\Rightarrow (\frac{-1+2}{2}, \frac{0+2}{2})= (\frac{3+x}{2}, \frac{1+y}{2})\\\\\Rightarrow (\frac{1}{2}, \frac{2}{2})= (\frac{3+x}{2}, \frac{1+y}{2})$

By comparing x and y co-ordinates on both sides, we get

$\Rightarrow \frac{3+x}{2}= \frac{1}{2}\ \ \ ,\ \ \ \frac{1+y}{2}= \frac{2}{2}\\\\\Rightarrow3+x=1\ \ \ ,\ \ \ 1+y=2\\\\\Rightarrow x=-2\ \ \ ,\ \ \ y=1$

$\boxed{The\ fourth \ vertex \ is \ D(-2,1)}$

Answer 2

Step-by-step explanation:

hello lam gourav Joshi