Question

The coordimates of one end of a diameter of a circle are (4,-1) and the coordinates of the
centre of the circle are (1,-3). Find the coordinate of the other end of the diameter,

Answer 1

GivEn:-

• Coordinates of one end of diameter of circle (A) = (4,-1)
• Let coordinates of another end of diameter (B) = (a,b)
• Coordinates of center of circle (C) = (1,-3)

To find:-

• Coordinates of another end of diameter

Solution:-

★ Center divides the diameter into two equal halves. So, we can also say that centre is the mid point of diameter of a circle and divides it into 1:1.

Using section Formula :-

$\large\bold{\underline{\underline{\boxed{\sf{\purple{ x = \dfrac{ \sf m_1 \sf x_2 + \sf m_2 \sf x_1 }{ \sf m_1 + \sf m_2 }}}}}}}$

$\ \ \ \ \ \ \ \ \ \ \ \ \ or$

$\large\bold{\underline{\underline{\boxed{\sf{\purple{ y = \dfrac{ \sf m_1 \sf y_2 + \sf m_2 \sf y_1 }{ \sf m_1 + \sf m_2 }}}}}}}$

Now,

$1 = \dfrac{a - 4}{2}$

$2 = a - 4$

$a = -2$

And,

$-3 = \dfrac{b - 1}{2}$

$-6 = b - 1$

$b = -5$

$\dag$ Therefore, Coordinates of B = (-2,-5).

____________________________________