Question

3). find the area of triangle formed by joining the
mid-points of the sides of the th triangle whose vertices are A(2,3) B (4, 4) & (2, 6)​

Answer 1

Given :

Vertices of triangle are : A(2, 3), B(4, -4) and C(2, 6)

Find :

Area of triangle.

Solution :

Continuing the Attachment..

We have coordinates :

→ D = (3, -1/2)

→ E = (3, 1)

→ F = (2, 9/2)

We know that..

Area of ΔABC :

We have..

= 2

= 4

= 2

= 3

= -4

= 6

Substitute the known values in above formula

∴ Area of ΔABC = 3 sq. units

Now,

Area of ΔDEF :

We have..

= 3

= 3

= 2

= -1/2

= 1

= 9/2

_____ (eq 2)

∴ Area of ΔDEF = 3/4 sq. units

If we have to find ratio.. then ratio :

→ Area of ΔDEF/Area of ΔABC = (3/4)/3

→ Area of ΔDEF/Area of ΔABC = 1/4

∴ Ratio is 1:4

But according to question we have to find the area of the triangle formed by joining the mid points.

And after joining mid points, we have ΔDEF.

✯ Answer :

Area of ΔDEF = 3/4 sq. units.