Question 15 of 18intermediate🔧 ApplyNumerical2 marks

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).

Correct Answer

(3, -10)

Exercise: EXERCISE 7.2 | Q: 7 | (Page 13)
For More Understanding

Explanation

This question tests the understanding that the center of a circle is the midpoint of its diameter. Students must apply the midpoint formula in reverse - given the midpoint and one endpoint, find the other endpoint. The context provides examples of using section formula and midpoint concepts in coordinate geometry problems.

Solution Steps

  1. Step 1: Since AB is the diameter and the centre is (2, -3), the centre is the mid-point of AB.

  2. Step 2: Let the coordinates of A be (x, y). Using the mid-point formula, the coordinates of the centre are: (x+12,y+42)=(2,−3)\left( \frac{x + 1}{2}, \frac{y + 4}{2} \right) = (2, -3)

  3. Step 3: Equating the x-coordinates: x+12=2\frac{x + 1}{2} = 2, so x+1=4x + 1 = 4, giving x=3x = 3.

  4. Step 4: Equating the y-coordinates: y+42=−3\frac{y + 4}{2} = -3, so y+4=−6y + 4 = -6, giving y=−10y = -10.

  5. Step 5: Therefore, the coordinates of point A are (3, -10).

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