Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
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.
Given:
The vertex of a triangle is $(1, 1)$ and the middle points of the sides through it are $(-2, 3)$ and $(5, 2)$.
To do:
We have to find other vertices.
Solution:
Let the coordinates of the vertex $A$ are $(1, 1)$ and the mid-points of $AB$ and $AC$ are $D (-2, 3)$ and $E (5, 2)$.
Let the coordinates of the other two vertices of the triangle be $B (x_1, y_1)$ and $C(x_2, y_2)$.
\( \mathrm{D} \) is the mid point of \( \mathrm{AB} \).
This implies,
The coordinates of \( \mathrm{D} (-2, 3)=(\frac{1+x_1}{2}, \frac{1+y_1}{2}) \)
\( \Rightarrow 2(-2)=1+x_1 \) and \( 2(3)=1+y_1 \)
\( \Rightarrow x_{1}=-4-1=-5 \) and \( y_{1}=6-1=5 \)
Coordinates of \( \mathrm{B} \) are $(-5,5)$.
Similarly,
\( \mathrm{E} \) is the mid-point of \( \mathrm{AC} \).
The coordinates of \( \mathrm{E} (5, 2)=(\frac{1+x_2}{2}, \frac{1+y_2}{2}) \)
\( \Rightarrow 1+x_{2}=5(2) \) and \( 1+y_{2}=2(2) \)
\( x_{2}=10-1=9 \) and \( y_{2}=4-1=3 \)
Coordinates of \( \mathrm{C} \) are $(9,3)$.
The other two vertices are $(-5,5)$ and $(9,3)$.
34 Views
