Ex.7.2 Q7 Coordinate Geometry Solution - NCERT Maths Class 10

Go back to  'Ex.7.2'


Find the coordinates of a point \(A\), where \(AB\) is the diameter of circle whose center is \((2, -3)\) and \(B\) is \((1, 4)\)


Text Solution



The coordinates of the point \(P(x, y)\) which divides the line segment joining the points \(A(x1, y1)\) and \(B(x2, y2)\), internally, in the ratio \(\rm m1 : m2\) is given by the Section Formula.

What is the known?

The \(x\) and \(y\) co-ordinates of the center of the circle and one end of the diameter \(B\).

What is the unknown?

The coordinates of a point \(A\).


From the Figure,


  • Let the coordinates of point \(A\) be \((x, y)\).
  • Mid-point of \(AB\) is \(C\) \((2, -3)\), which is the center of the circle.

\(\begin{align} \therefore \; (2, - 3) &= \left( {\frac{{{\text{x}} + 1}}{2},\frac{{{\text{y}} + 4}}{2}} \right)   \end{align}\)

\(\begin{align}  \Rightarrow \frac{{{\text{x}} + 1}}{2}& = 2{\text{ and }}\frac{{{\text{y}} + 4}}{2} = - 3 & &  \end{align}\) (By Cross multiplying & transposing)

\(\begin{align}  \Rightarrow {\text{x}} + 1 &= 4{\text{ and y}} + 4 = - 6  \end{align}\)

\(\begin{align}  \Rightarrow {\text{x}} &= 3{\text{ and y}} = - 10\end{align}\) 

Therefore, the coordinates of \(A\) are \((3, -10)\)


Frequently Asked Questions

What are Class 10 NCERT Exemplars?
While getting good scores in school tests is a desirable outcome, it is not a reliable indicator of how strong your child’s math foundation really is. Many students who score well in school exams in their earlier years, might struggle with math in higher grades because of a weak foundation. At Cuemath, we evaluate your child’s grasp of math fundamentals, and take corrective actions immediately. Also, your child may have limited exposure in their school, and in most cases, may not feel challenged to learn more. Cuemath's customised learning plan ensures your child is challenged with varied difficulty levels of questions at every stage.
What is the difference between CBSE and NCERT syllabus for Class 10?
How will Class 10 NCERT books help in exam preparation?
How will Class 10 NCERT books help you understand basic math concepts?
Which is the best video solution for the class 10 maths NCERT?