Question

Find the coordinates of a point P, where PQ is the diameter of a circle whose centre is (2, -3) and Q is (1, 4).

Answer 1

Answer:

p=(3, -10)

Step-by-step explanation:

I hope you understood

Answer 2

Given:

The coordinates of the center and a point Q on the circle are (2,-3) and (1,4).

To Find:

The coordinates of the point P if PQ is the diameter of the circle.

Solution:

The given problem can be solved by using the concepts of circles.

1. It is given that coordinates of the center of the circle are (2,-3), PQ is one of the diameters to the given circle. The Coordinates of point Q are (1,4).

2. A circle is defined as the collection of points that are equidistant from a fixed point. The distance between the fixed point and the circle boundary is defined as its radius.

3. The radius of the given circle is$\sqrt{(2-1)^2+(-3-4)^2}$,

=> Radius of given circle =$\sqrt{50}$ units.

4. The distance between the x-coordinates of Q and center is 1 unit, the distance between y-coordinates of Q and center is 7 units.

5. According to the properties of circles, the coordinates of the center of the circle can be obtained by taking the midpoint of the coordinates of the diameter.

6. Let the coordinates of P be (x,y), According to the property mentioned in point 5,

=> ( x + 1 )/2 = 2 and ( y + 4 )/2 = -3,

=> x = 4 - 1, y = -6 -4,

=> x = 3, y = -10.

Therefore, the coordinates of the point P are (3,-10).