Ex 7.2, 7
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).
Let the circle be as shown with centre C (2, −3)
Let AB be the diameter of the circle
Since AB is the diameter,
Centre C must be the mid−point of AB
Let A(x, y)
Since C is the mid−point of AB
x−coordinate of C = (𝑥1 + 𝑥2)/2
y−coordinate of C = (𝑦1 + 𝑦2)/2
Where
x1 = x, y1 = y
x2 = 1, y2 = 4
Hence the coordinates of A(x , y)
= A(3, −10)
x−coordinate of C = (𝑥 + 1)/2
2 = (𝑥 + 1)/2
2 × 2 = x + 1
4 = x + 1
4 – 1 = x
3 = x
x = 3
y−coordinate of C = (𝑦 + 4)/2
−3 = (𝑦 +4)/2
−3 × 2 = y + 4
−6 = y + 4
−6 – 4 = y
−10 = y
y = −10

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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