BITSAT 2006 Solved Question Paper

Let the points be B(x1,y1) and D(x2,y2) mid point of
BD=(

x1+x2

2

,

y1+y2

2

) and mid point of AC=(0,1)
We know, mid point of both the diagonal lie on the same point E.
⇒

x1+x2

2

−0 and

y1+y2

2

=1
⇒x1+x2=0 ...(i)
and y1+y2=2 ...(ii)
Slope of BD× slope of AC=−1

(y1−y2)

(x1−x2)

×

(3+1)

(0−0)

=−1
⇒y1−y2=0 ...(iii)
Now, slope of AB× slope of BC=−1
⇒

(y1+1)

(x1−0)

×

(y1−3)

(x1−0)

=−1
⇒(y1+1)(y1−3)=−x12
⇒2(−2)=−x12 ‌‌‌‌‌‌ [∵y1=1]
⇒x1=±2
∴ The required points are (2,1) and (−2,1).