In triangle ABC, the midpoints of the sides AB, BC and AC are (1,4) , (2,0) and (-4,1) , respectively. Find the coordinates of points A, B and C.

The coordinates are A(-5,3), B(7,1) and C(-3,-1).

Step-by-step explanation:

Given,

The midpoints of the sides AB, BC and AC are (1,4) , (2,0) and (-4,1) respectively.

To find the coordinates of A, B, C.

Let,

The coordinates of A,B and C are (a,x), (b,y) and (c,z) respectively.

Formula

The mid point of two given points () and () is ()

Now,

= 1 and = 4 ⇒ a+b = 2 ---(1) and x+y = 4 --(2)

= 2 and = 0 ⇒ b+c = 4 ---(3) and y+z = 0---(4)

= -4 and = 1 ⇒ c+a = -8 ---(5) and z+x = 2 ----(6)

Adding (1), (3) and (5) we get,

2(a+b+c) = -2

or, a+b+c = -1

So, a = -5, b = 7 and c = -3

Similarly Adding (2), (4) and (6) we get,

2(x+y+z) = 6

or, x+y+z = 3

So, x = 3, y = 1 and z = -1

Hence,

The coordinates are A(-5,3), B(7,1) and C(-3,-1).

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step-by-step explanation:

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