Question

The centre of the circle is (0,0).Verify if one end of the diameter is (2-3) then second point is (-2,3)

Answer 1

Answer:

Verified

Step-by-step explanation:

Center of circle (0,0)

One end of Diameter (2,-3)

So radius = $\sqrt{(2-0)^2 + (-3-0)^2}$

=> radius = $\sqrt{4 + 9}$

=> radius = $\sqrt{13}$

if second end of diameter = (-2, 3)

Then it should be at a distance of radius from center (0,0)

and at a distance of diameter from other end (2 , -3)

Distance from Center = $\sqrt{(-2-0)^2 + (3-0)^2}$

=> Distance from Center = $\sqrt{4 + 9}$

=> Distance from Center = $\sqrt{13}$

=> Distance from Center = Radius

condition 1 is met

Distance from other end = $\sqrt{(-2-2)^2 + (3-(-3))^2}$

=>Distance from other end = $\sqrt{(-4)^2 + (6)^2}$

=>Distance from other end = $\sqrt{(-4)^2 + (6)^2}$

=>Distance from other end = $\sqrt{16 +36}$

=>Distance from other end = $\sqrt{52}$

=>Distance from other end = $2\sqrt{13}$

=>Distance from other end = 2 × Radius

=>Distance from other end = Diameter

Condition 2 is also met.

Hence it is verified that second end of diameter (-2,3)