Question

centre of circle is (3,-4) and one end point of diameter is (1,4) then find another end point of diameter

Answer 1

Since the circle’s center is at the origin, this would make our calculation much easier. Since we know where one point of the diameter ends (-3, -4), this tells us that by the distance formula:

center-endpt = sqrt[(-3 - 0)^2 +(-4 - 0)^2]
center-endpt = sqrt[(-3)^2 + (-4)^2]
center-endpt = sqrt(9 + 16)
center-endpt = sqrt(25)
center-endpt = 5

This distance however is from the center to one of the endpoints. The diameter is twice this distance, so this tells us the diameter is 10.

Answer 2

$let \: the \: other \: point \: be \: x \\ therefor \: \sqrt{ {(x - 3)}^{2} } + \sqrt {( - 4 - y)}^{2} = \sqrt{ (3 - 1 } )^{2} + \sqrt{ {(4 - 4)}^{2} } \\ \sqrt{x { }^{2} + 9 - 6x } + \sqrt{16 + {y}^{2} - 8y} = 4$