Question

Find the area of ABC where A(1,-4) and midpoints of the sides through A being (2,-1) and (0,-1)

Answer 1

Triangle ABC has three points, A,B & C.

Coordinates of A is : .

Midpoint of AB is:

Midpoint of AC is:

We need to find the area of the triangle.

Let coordinates of point B be .

Mid point of AB is :

But since mid point of AB is

Thus,

Coordinates of point B is : .

 Let Coordinate of point C be

Mid point of AC is :

But since mid point of AC is

Thus,

Coordinates of point C is : .

 Area of a triangle whose vertices are is:

Area

In the given case, corresponds to B, corresponds to C, and corresponds to A. 

Hence area of the triangle =

Hence, area of the triangle is sq.units.

Answer 2

As the mid points from the point A are(2,-1) & (0,-1). From this we can find the point B and C by using mod point formula x1 + x2 /2 which are... B(3,2) and C(-1,2) . Then we will apply area formula..... We will get the answer as 12 Sq. Units