Name: Coordinates of Centroid
Uploaded: 2019-07-19
Duration: 3 min 16 s
Description: This video discusses how we can find the coordinates of the centroid using the coordinates of the three vertices given. Watch and learn the concept.

Question

If a vertex of a triangle be

(1, 1)

and the mid-pints of the sides through it be

(- 2, 3)

and

(5, 2)

. Find the other vertices.

Accepted Answer

Given, a vertex of a triangle be $(1, 1)$ and the mid-pints of the sides through it be $(- 2, 3)$ and $(5, 2)$ .
According to the given information, we draw the following figure.

We have to find the coordinates of the vertices $B$ and $C$ .

Let, the coordinates of $B$ and $C$ are $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ respectively.

Let $D (- 2, 3)$ be the mid-point of the side $A B$ , then applying the mid-point formula, we get,

The coordinates of $D (- 2, 3) = (\frac{1 + x_{1}}{2}), (\frac{1 + y_{1}}{2})$

or $- 2 = (\frac{1 + x_{1}}{2}) \Rightarrow 1 + x_{1} = - 4 \Rightarrow x_{1} = - 5$

and $3 = (\frac{1 + y_{1}}{2}) \Rightarrow 1 + y_{1} = 6 \Rightarrow y_{1} = 5$

Similarly, let $E (5, 2)$ be the mid-point of the side $A C,$ then applying the mid-point formula, we get,

The coordinates of $E (5, 2) = (\frac{1 + x_{2}}{2}), (\frac{1 + y_{2}}{2})$

or $5 = (\frac{1 + x_{2}}{2}) \Rightarrow 1 + x_{2} = 10 \Rightarrow x_{2} = 9$

and $2 = (\frac{1 + y_{2}}{2}) \Rightarrow 1 + y_{2} = 4 \Rightarrow y_{2} = 3$

Hence, the coordinates of the other vertices are $B (- 5, 5)$ and $C (9, 3)$ .

If a vertex of a triangle be $(1, 1)$ and the mid-pints of the sides through it be $(- 2, 3)$ and $(5, 2)$ . Find the other vertices.

Important Questions on Section and Mid-Point Formulae

Learn and Prepare for any exam you want !

If a vertex of a triangle be (1, 1) and the mid-pints of the sides through it be (-2, 3) and (5, 2). Find the other vertices.

Important Questions on Section and Mid-Point Formulae

Learn and Prepare for any exam you want !

If a vertex of a triangle be $(1, 1)$ and the mid-pints of the sides through it be $(- 2, 3)$ and $(5, 2)$ . Find the other vertices.