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)
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 m₁ : m₂ is given by the section formula.
Let the coordinates of point A be (x, y).
Mid-point of AB is (2, - 3), which is the center of the circle.
According to the mid point formula,
O(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
We have A(x, y) and B(1, 4) and the center is (2, -3)
Therefore by using midpoint formula,
(2, -3) = [(x + 1) / 2, (y + 4) / 2]
⇒ (x + 1) / 2 = 2 and (y + 4) / 2 = - 3 (By Cross multiplying & transposing)
⇒ x + 1 = 4 and y + 4 = - 6
⇒ x = 3 and y = - 10
Therefore, the coordinates of A are (3, - 10)
☛ Check: NCERT Solutions for Class 10 Maths Chapter 7
Video Solution:
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).
NCERT Class 10 Maths Solutions Chapter 7 Exercise 7.2 Question 7
Summary:
The coordinates of a point A, where AB is the diameter of a circle whose centre is (2, - 3) and B is (1, 4) is (3, -10).
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