Question

ab is the diameter of a circle with centre (2,2) if coordinates of a point a are (2,-1) then find coordinates of point b​

Answer 1

$\underbrace{\underline{\bf \bigstar \:Required\: Answer\::}}$

» We are given with the coordinates of the centre of the circle and the coordinates of one end of the diameter AB.

» Let the centre of the circle be O.

» We know that radius of the circle is half the diameter of the same circle .

» As the centre is the midpoint of the diameter so, we would use the section formula to find the coordinates of the point B.

◑ Consider the attachment as the figure of the question .

• Let the coordinates of the point B = $\sf(x_1, y_1)$.

◑ According to section formula :

$\Rightarrow\:\boxed{\sf x~coordinate =\dfrac{x_1+x_2}{2}}$

$\Rightarrow\:\boxed{\sf y~coordinate =\dfrac{y_1+y_2}{2}}$

For this question,

• $\sf x_2= 2$
• $\sf y_2=-1$
• $\sf x = 2$
• $\sf y = 2$

$\colon \longrightarrow \sf \: x = \dfrac{x _{1} + x _{2} }{2}$

$\colon \longrightarrow \sf \:2 = \dfrac{x _{1} +2 }{2}$

$\colon \longrightarrow \sf \: 4 = x _{1} + 2$

$\colon \implies \boxed{ \red{ \bf{{ \tt{x}} _{1} = 2}}} \: \purple \bigstar$

And

$\\ \colon \longrightarrow \sf \: y = \dfrac{y _{1} + y _{2} }{2}$

$\colon \longrightarrow \sf \: 2 = \dfrac{y _{1} + ( - 1)}{2}$

$\colon \longrightarrow \sf \: 4 = y_{1} - 1$

$\colon \implies \boxed{ \bf{ \pink{{ \tt{y}} _{1} = 5}}} \: \purple \bigstar$

$\green\therefore\underline{\sf The\:coordinates\:of\:B=\bf{(2, 5) }}$

_____________________________

Answer 2

$\underbrace{\underline{\bf \bigstar \:Required\: Answer\::}}$

» We are given with the coordinates of the centre of the circle and the coordinates of one end of the diameter AB.

» Let the centre of the circle be O.

» We know that radius of the circle is half the diameter of the same circle .

» As the centre is the midpoint of the diameter so, we would use the section formula to find the coordinates of the point B.

◑ Consider the attachment as the figure of the question .

Let the coordinates of the point B = $\sf(x_1, y_1)$.

◑ According to section formula :

$\Rightarrow\:\boxed{\sf x~coordinate =\dfrac{x_1+x_2}{2}}$

$\Rightarrow\:\boxed{\sf y~coordinate =\dfrac{y_1+y_2}{2}}$

For this question,

$\sf x_2= 2$

$\sf y_2=-1$

$\sf x = 2$

$\sf y = 2$

$\colon \longrightarrow \sf \: x = \dfrac{x _{1} + x _{2} }{2}$

$\colon \longrightarrow \sf \:2 = \dfrac{x _{1} +2 }{2}$

$\colon \longrightarrow \sf \: 4 = x _{1} + 2$

$\colon \implies \boxed{ \red{ \bf{{ \tt{x}} _{1} = 2}}} \: \purple \bigstar$

And

$\\ \colon \longrightarrow \sf \: y = \dfrac{y _{1} + y _{2} }{2}$

$\colon \longrightarrow \sf \: 2 = \dfrac{y _{1} + ( - 1)}{2}$

$\colon \longrightarrow \sf \: 4 = y_{1} - 1$

$\colon \implies \boxed{ \bf{ \pink{{ \tt{y}} _{1} = 5}}} \: \purple \bigstar$

$\green\therefore\underline{\sf The\:coordinates\:of\:B=\bf{(2, 5) }}$