Question

If a vertex of a triangle be (1, 1) and the middle points of the sides through it be (–2, 3) and (5, 2), find the other vertices.

Answer 1

Let a ΔABC in which P and Q are the mid-points of sides AB and AC respectively. The coordinates are A (1, 1); P (−2, 3) and Q (5, 2).

We have to find the co-ordinates of `B(x_1,y_1)` and `C(x_2,y_2)`.

In general to find the mid-point P(x,y) of two points `A(x_1,y_1) `and `B(x_2,y_2)` we use section formula as,

`P(x,y) = ((x_1 + x_2)/2, (y_1 + y_2)/2)`

Therefore mid-point P of side AB can be written as,

`P(-2, 3) = ((x_1 + 1)/2, (y_1 + 1)/2)`

Now equate the individual terms to get,

`x_1 = -5`

`y_1 = 5`

So, co-ordinates of B is (−5, 5)

Similarly, mid-point Q of side AC can be written as,

`Q(5, 2) = ((x_2 + 1)/2, (y_2 + 1)/2)`

Now equate the individual terms to get,

`x_2 = 9`

`y_2 = 3`

So, co-ordinates of C is (9, 3).