Question

what is the other end of diameter of a circle whose center 1, 2 and one end point of the diameter is 3, 4

Answer 1

$\huge\bf\pink{\mid{\overline{\underline{Your\: Answer}}}\mid}$

______________

______

B = (-1,0)

______

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step-by-step explanation:

Given,

a circle

whose centre is point O.

also,

let,

AB be its diameter

then,

also,

given that,

coordinates of

A = (3,4)

O = (1,2)

and,

let,

B = (x,y)

Now,

AB is the diameter,

therefore,

AO = BO = radius

Therefore,

O is the bisector of AB.

therefore,

by section formula,

sum of coordinate of x axis of A and B

= 2( coordinate of x axis of centre O)

=> 3+ x = 2×1

=> x = 2-3

=> x = -1

Similarly,

sum of coordinate of y axis of A and B

= 2( coordinate of y axis of centre O)

=> 4 + y = 2×2

=> y = 4 -4

=> y = 0

Hence,

the coordinate of other end of diameter,

B = (-1,0)

_____

___________

________________

Answer 2

$\huge\underline\mathfrak{Answer:-}$

$<b>Given,$

a circle whose centre is point O.

also,

let, AB be its diameter

then,

also,

given that,

coordinates of A = (3,4)

O = (1,2)

and,

let, B = (x,y)

Now,

AB is the diameter,

therefore,

AO = BO = radius

Therefore,

O is the bisector of AB.

therefore,

by section formula,

sum of coordinate of x axis of A and B

= 2( coordinate of x axis of centre O)

=> 3+ x = 2×1

=> x = 2-3

=> x = -1

Similarly,

sum of coordinate of y axis of A and B

= 2( coordinate of y axis of centre O)

=> 4 + y = 2×2

=> y = 4 -4

=> y = 0

Hence,

the coordinate of other end of diameter,

$\boxed{B = (-1,0)}$

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