Question

If one end of a circle is (4,6) and the centre is (-4,7), then the other end is?(No spamming)​

Answer 1

question is simple to solve using section formula for the midpoint.

Your Answer is in attachment !

Answer 2

$\huge{\bf{\green{\mathfrak{Question:-}}}}$

• If one end of a circle is (4,6) and the centre is (-4,7), then the other end is?

$\huge {\bf{\orange{\mathfrak{Answer:-}}}}$

• $\textsf{According to the question, in a circle diameter is given.}$

• $\textsf{We know that one end is (4,6) and the centre of the circle is (- 4,7).}$

• $\textsf{Let the other end (coordinates) be (x, y).}$

• $\textsf{We know that,}$

• $\boxed{\sf Midpoint \: formula \: = \: \dfrac{x_{1} \: + \: x_{2}}{2} \: \: , \: \: \dfrac{y_{1} \: + \: y_{2}}{2}.}$

• $\sf (- \: 4,7) \: = \: \dfrac{4 \: + \: x}{2} \: \: , \: \: \dfrac{6 \: + \: y}{2}$

• $\textsf{Equating the coordinates,}$

• $\sf - \: 4 \: = \: \dfrac{4 \: + \: x}{2} \: \: , \: \: 7 \: = \: \dfrac{6 \: + \: y}{2}$

• $\sf - \: 4 \: * \: 2\: = \: 4 \: + \: x\: \: , \: \: 7 \: * \: 2 \: = \: 6 \: + \: y$

• $\sf - \: 8 = \: 4 \: + \: x\: \: , \: \: 14 \: = \: 6 \: + \: y$

• $\sf - \: 8 \: - \: 4 \: = \: x\: \: , \: \: 14 \: - \: 6 \: = \: y$

• $\boxed{\sf x \: = \: - \: 12 \: \: , \: \: y \: = \: 8.}$

$\huge{\bf{\red{\mathfrak{Conclusion:-}}}}$

• $\boxed{\therefore{\textsf{ The other end (coordinates) = (- 12,8).}}}$

$\huge{\bf{\purple{\mathfrak{Formulas\: used:-}}}}$

• $\sf Midpoint \: formula \: = \: \dfrac{x_{1} \: + \: x_{2}}{2} \: \: , \: \: \dfrac{y_{1} \: + \: y_{2}}{2}.$