AP EAPCET 04-Jul-2022 Shift 1 Paper

AB=a,BC=b,DA=a−b
In △ABC, using vector concept, we have
⇒AB+BC‌=AC
AC‌=a+b.....(i)In △ADC,
‌AD+DC=AC
‌⇒DC=AC−AD
‌=a+b−(b−a)=2a
In △MDC
‌MD+DC=MC
⇒‌‌MD=‌

b

2

−2a [ ∵ M is mid-point of B C]
In △ADX,
AD‌+DX=AX
AD‌+‌

4

5

DM=AX
⇒‌‌AX‌=b−a+‌

4

5

(2a−‌

b

2

)
‌=b−a+‌

8

5

a−‌

2

5

b=‌

3

5

(a+b)
⇒‌‌AX=‌

3

5

AC
[from Eq. (i)]
which says that AX|AC and one point A is common there.
Therefore, A,X and C are collinear.