Question

If (0,0) is the center of a circle and (2, 3) is one end point of its diameter, then find the other end point​

Answer 1

Centre of circle = o(0,0)

One end of diameter = (2,3)

Let other end of diameter be (a,b)

We know that , centre of circle lies on midpoint diameter.

Therefore, O(0,0) is midpoint of line joining (2,3) and (a,b)

$\longrightarrow \rm(0,0) = \rm \bigg( \dfrac{2 + a}{2} ,\dfrac{3 + b}{2} \bigg)$

$\longrightarrow \rm0 = \rm \dfrac{2 + a}{2} \\ \\\rm0 = \rm {2 + a} \\ \\\rm - 2= \rm a\\ \\ \\ \longrightarrow \rm0= \rm \dfrac{3 + b}{2} \\ \\ \longrightarrow \rm0= \rm {3 + b}\\ \\ \longrightarrow \rm - 3= \rm b$

Therefore , co-ordinates of other end of diameter = (-2,-3)

Additional Information :

Co-ordinates of midpoint of line joining (a,b) and (c,d) is given as :-

$\rm \implies \bigg( \dfrac{a + c}{2} \: , \: \dfrac{b + d}{2} \bigg)$

Answer 2

${\large{\bold{\sf{\underline{Understanding \; the \; question}}}}}$

➦ This question says that is (0,0) is the center of a circle ; circle's centre lie on the diameter and (2, 3) is one end point of its diameter, then we have to find the other end point.

${\large{\bold{\sf{\underline{Given \; that}}}}}$

➦ (0,0) is the center of a circle

➦ (2, 3) is one end point of its diameter

${\large{\bold{\sf{\underline{To \; find}}}}}$

➦ The other end ppoint of it's diameter

${\large{\bold{\sf{\underline{Solution}}}}}$

➦ The other end point of it's diameter = (-2,-3)

${\large{\bold{\sf{\underline{Assumptions}}}}}$

➦ Let (x,y) as the other end point of it's diameter.

${\large{\bold{\sf{\underline{Full \: Solution}}}}}$

➨ (0,0) = ${\bold{\sf{( \dfrac{2 + x}{2} , \dfrac{3 + y}{2} )}}}$

Now, firstly

➨ 0 = ${\bold{\sf{\dfrac{2 + x}{2}}}}$

➨ 0 = 2 + x

➨ 0 - 2 = x

➨ -2 = x

➨ x = -2

Now

➨ 0 = ${\bold{\sf{\dfrac{3 + y}{2}}}}$

➨ 0 = 3 + y

➨ 0 - 3 = y

➨ -3 = y

➨ y = -3

• Henceforth, (-2,-3) is the other end point of it's diameter

( Diagram of this question is in attachment )