Question

Find the coordinates of a point A, where AB is diameter of a circle whose
centre is (2, -3) and B is the point (1,4).

can anyone tell​

Answer 1

Answer:

coordinates of point A is ( 3, -10)

Step-by-step explanation:

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Answer 2

$\underline{\boxed{\bold{Question}}}$  

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❏ Find the coordinates of a point A, where AB is diameter of a circle whose  center is (2, -3) and B is the point (1,4).

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$\underline{\boxed{\bold{Important\;Information}}}$  

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❏ Circle is 2-D shape which has a center and length of all point from center are located at equal distance called radius.

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Here is unique relation between radius and diameter :

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$\boxed { \bold { \red {:\leadsto \; Radius = \dfrac{Diameter}{2} }}}$

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$\underline{\boxed{\bold{Given}}}$

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❏ Center = (2, -3)

❏ Point B = (1, 4)

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$\underline{\boxed{\bold{Answer}}}$

Let's Start !

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As we know that center is located at equal distance from 2 diametric points, so we will use section formula for mid-point !

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As we know that both points are at equal distance

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∴ PA = PB

∴ Ratio = 1 : 1

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PART : 1

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• Let's find x-coordinate of point A

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As center (2 , -3) lies at mid point of between point A(x , y) and point B(1 ,4) :

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$\boxed { \bold { \red { :\implies 2 = \dfrac{x + 1}{2} } } }$

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$\bold { \blue { :\implies (2 \times 2) = x + 1 } }$

$\bold { \orange { :\implies x = (2 \times 2)- 1 } }$

$\bold { \blue { :\implies x = 4- 1 } }$

$\bold { \orange{ :\implies x = 3} }$

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∴ x-coordinate of point A = 3

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PART : 2

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• Let's find y-coordinate of point A

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As center (2 , -3) lies at mid point of between point A(x , y) and point B(1 ,4) :

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$\boxed { \bold { \red { :\implies -3 = \dfrac{y + 4}{2} } } }$

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$\bold { \blue { :\implies (-3 \times 2) = y+ 4 } }$

$\bold { \orange { :\implies y = (-3 \times 2)- 4 } }$

$\bold { \blue { :\implies y = -6 - 4 } }$

$\bold { \orange{ :\implies y = (-10)} }$

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∴ y-coordinate of point A = (-10)

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$\boxed{\boxed{\bold{\therefore Coordinates \; of \; point \; A = (3,-10)}}}$

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Hope this helps u.../

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