Q. 114.9( 14 Votes )

Find the area of

Answer :


To find the area of the triangle ABC, we first find the coordinates of points B and C.


P(2,-1) is the midpoint of AB.


Midpoint of AB:


x- coordinate = (x1 + x2) / 2


2 = (1 + x ) / 2


4 = 1 + x


x = 3


y-coordinate = (y1 + y2) / 2


-1 = (-4 + y ) / 2


-2 = -4 + y


y = 2


Midpoint of AC:


x- coordinate = (x1 + x2) / 2


0 = (1 + z ) / 2


0 = 1 + z


z = -1


y-coordinate = (y1 + y2) / 2


-1 = (-4 + t ) / 2


-2 = -4 + t


t = 2


Therefore, B(3,2) and C(-1,2) and we know A(1,-4) already.
Now, we find the area of ΔABC,




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