If The coordinates of the mid points of a triangle are (1,2) (0,-1) and(2,-1). Find the coordinated of it's vertices

Hello Dyaga

Here is the solution:

The three given points are the midpoints of the sides of a triangle. Let them be:

$D(1,2), E(0,-1), F(2,-1)$ $D(1,2),E(0,-1),F(2,-1)$

We use the standard relation between vertices and midpoints:

If $D, E, F$ are midpoints of sides $B C, C A, A B$, then:

$\begin{aligned} & \text { - } A=E+F-D \\ & \text { - } B=D+F-E \\ & \text { - } C=D+E-F\end{aligned}$ $C=D+E-F$

1. Vertex A:

$\begin{gathered}A=(0,-1)+(2,-1)-(1,2) \\ A=(0+2-1,-1-1-2)=(1,-4)\end{gathered}$

2. Vertex B:

$\begin{gathered}B=(1,2)+(2,-1)-(0,-1) \\ B=(1+2-0,2-1+1)=(3,2)\end{gathered}$

3. Vertex C:

$\begin{gathered}C=(1,2)+(0,-1)-(2,-1) \\ C=(1+0-2,2-1+1)=(-1,2)\end{gathered}$

The coordinates of the triangle's vertices are: $(1,-4),(3,2),(-1,2)$

$(1,-4),(3,2),(-1,2)$