Question

If D(1,2),E(1,0) and F(0,1) are midpoint of sides BC,AC and AB respectively of ABC,find the coordinates of point A,B and C​

Answer 1

Let us assume the points be B (p, q), C (r, s) and F (x, y)

It is clear that, mid-point of AB = Coordinates of D

∴ p = 2

Also,

- 1 + q = 0

q = 1

∴ Points of B is (2, 1)

Similarly, mid-point of AC = Coordinates of E

∴ r = 0

And,

- 1 + s = 2

s = 3

∴ Points of C is (0, 3)

Also, Coordinates of F = Mid-point of BC

= (1, 2)

∴ Points of F is (1, 2)

We know that,

= 4 square units

Also,

.

.

= 1 square unit (As area cannot be negative)