UPSC NDA Math Model Paper 1

Given , the three vertices of the parallelogram ABCD are A(1, a), B(3, a), C(2, b).
Here AB || CD
Slope of AB = Slope of CD
Slope of parallel lines are equal.and if (x1,y1)‌and(x2,y2) are two points then the slope of the line is given by m=

y2−y1

x2−x1

⇒

a−a

3−1

=

b−y

2−x

⇒0=

b−y

2−x

⇒b=y
Now, AD || BC
Slope of AD = Slope of BC
Slope of parallel lines are equal.and if (x1,y1)‌and(x2,y2) are two points then slope of the line is given by m=

y2−y1

x2−x1

⇒

a−y

1−x

=

a−b

3−2

Here, b=y
⇒1−x=1
⇒x=0
Hence D=(0,b)