Question

Points A, B, and C are collinear. Point B is between A and C. Find the length of AB.
AC = x+21, BC = 6, AB = 2x+24

Answer 1

Answer:

Correct option is

A

(1, 6)

If three points P(x

1

,y

1

),Q,R(x

2

,y

2

) are collinear.

⇒PQ=QR and Q is the midpoint of PR

The mid point Q=(

2

x

1

+x

2

,

2

y

1

+y

2

)

Given, the points A(5,2),B(3,4) and C(x,y) are collinear and AB=BC

⇒ B is the mid-point of AC.

Using midpoint formula,

(

2

x+5

,

2

y+2

)=(3,4)

⟹

2

x+5

=3 and

2

y+2

=4

⟹x+5=6 and y+2=8

⟹x=1 and y=6

Hence, the coordinates of C are (1,6).