In Fig. 6, ABC is a triangle coordinates of whose vertex A are (0, -1). D and E respectively are the mid-points of the sides AB and AC and their coordinates are (1, 0) and (0, 1) respectively. If F is the mid-point of BC, find the areas of.

Question

Philoid · Accepted Answer

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)