Question

If P(4, -3) is a point that lies on the circumference of a circle on a cartesian plane with origin ‘O’ as its centre, which of the following points would lie on the circumference?

• A. (0, -5)
• B. (0, 4)
• C. (-3, 3)
• D. (5, 4)

Answer 1

The correct option is A (0, -5)

Given, point P(4, -3) lies on the circumference of a circle and centre of the circle lies at O(0, 0).
So, radius of the circle = OP = $\sqrt{{(-3-0)}^2+{(4-0)}^2}=\sqrt{9+16}=\sqrt{25}=5$ units
So, all the points lying on the circumference of the circle will be 5 units from the origin.

Distance of point (-3, 3) from O(0, 0) $=\sqrt{{(-3-0)}^2+{\left(3-0\right)}^2}=\sqrt{9+9}=\sqrt{18}=3\sqrt{2}$ units

Distance of point (0, 4) from O(0, 0) $=\sqrt{{(0-0)}^2+{\left(4-0\right)}^2}=\sqrt{16}=4$ units

Distance of point (0, -5) from O(0, 0) = $=\sqrt{{(0-0)}^2+{\left(-5-0\right)}^2}=\sqrt{25}=5$ units

Distance of point (5, 4) from O(0, 0) = $=\sqrt{{(5-0)}^2+{\left(4-0\right)}^2}=\sqrt{25+16}=\sqrt{41}$ units

Therefore, point (0, -5) lies on the circumference of the circle.