- Trending Categories
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
Find the coordinates of a point A where AB is diameter of a circle whose center is $( 2,\ -3)$ and B is the point $( 1,\ 4)$.
Given: AB is diameter of a circle whose centre is $( 2,\ -3)$ and B is the point $( 1,\ 4)$.
What to do: To Find the coordinates of a point A.
Solution:
Let the centre be O and co-ordinates of point A be $( x,\ y)$
$\because AB is the diameter of Circle with centre O.
$\therefore O is the mid-point of AB.
As known if we have two points $( x_{1},\ y_{1})$ and $( x_{2},\ y_{2})$
Then mid-point $=( \frac{x_{1}+x_{2}}{2},\ \frac{y_{1}+y_{2}}{2})$
Using the mid-point formula,
$( 2,\ -3)=( \frac{x+1}{2},\ \frac{y+4}{2})$
$\Rightarrow \frac{x+1}{2}=2$ and $\frac{y+4}{2}=-3$
$\Rightarrow x+1=4$ and $y+4=-3$
$\Rightarrow x=4-1$ and $y=-3-4$
$\Rightarrow x=3$ and $y=-7$
Hence, Co-ordinates of $A=( 3,\ -7)$
- Related Articles
- Find the coordinates of a point A, where AB is a diameter of the circle whose centre is $(2, -3)$ and B is $(1, 4)$.
- Find the coordinates of a point $A$, where $AB$ is the diameter of a circle whose centre is $(2, -3)$ and $B$ is $(1, 4)$.
- If A and B are points $(-2, -2)$ and $(2, -4)$ and P is a point lying on AB such that AP = $\frac{3}{7}$ AB, then find coordinates of P.
- In the given figure, a circle with center O is given in which a diameter AB bisects the chord CD at a point E such that $CE=E D=8 cm$ and $E B=4 cm$. Find the radius of the circle."\n
- In the figure, $PQ$ is a tangent at a point C to a circle with center O. if AB is a diameter and $\angle CAB\ =\ 30^{o}$, find $\angle PCA$."\n
- Find the coordinates of the point which divides the join of $(-1, 7)$ and $(4, -3)$ in the ratio $2: 3$.
- The centre of a circle is \( (2 a, a-7) \). Find the values of \( a \) if the circle passes through the point \( (11,-9) \) and has diameter \( 10 \sqrt{2} \) units.
- Find the circumference of a circle whose diameter is $10.5\ m$.
- The centre of a circle is $( -6,\ 4)$. If one end of the diameter of the circle is at $( -12,\ 8)$, then find the point of the other end.
- If the coordinates of points A and B are $( -2,\ -2)$ and $( 2,\ -4)$ respectively, find the coordinates of P such that \ $AP=\frac{3}{7} AB$, where P lies on the line segment AB.
- Find the length of the diameter of a circle whose circumference is $44\ cm$.
- If the coordinates of the one end of a diameter of a circle are $( 2,\ 3)$ and the coordinates if its center are $(-2,\ 5)$, then the coordinates of the other end of the diameter are:$( A)( -6,\ 7)$ $( B)( 6,\ -7)$ $( C)( 6,\ 7)$ $( D)( -6,\ -7)$
- $A (4, 2), B (6, 5)$ and $C (1, 4)$ are the vertices of $\triangle ABC$.Find the coordinates of point P on AD such that $AP : PD = 2 : 1$.
- Find a point which is equidistant from the point $A (-5, 4)$ and $B (-1, 6)$. How many such points are there?
- $ABC$ is a triangle. $D$ is a point on $AB$ such that $AD = \frac{1}{4}AB$ and $E$ is a point on $AC$ such that $AE = \frac{1}{4}AC$. Prove that $DE =\frac{1}{4}BC$.
Advertisements