Question

find the coordinates of a
point A, where AB is the
diameter of a circle whose
Centre is (2,-3) and
B is (1,4)​

Answer 1

Answer:-

Given:

AB is the diameter of a circle with center (2 , - 3) and B = (1 , 4).

Centre of the circle will be the midpoint of AB.

We know that,

Midpoint of a line segment joining the points (x₁ , y₁) , (x₂ , y₂) is :

$\sf \large \: (x \: ,\: y) = \bigg( \dfrac{x_{1} + x_{2} }{2} \: \: , \: \: \dfrac{y_{1} + y_{2} }{2} \bigg)$

Let,

• x = 2
• y = - 3
• x₂ = 1
• y₂ = 4.

Let the co - ordinates of A be (x₁ , y₁).

Hence,

$\implies \sf \: \: (2\: , \: - 3) = \bigg( \dfrac{x_{1} + 1}{2} \: \: , \: \: \dfrac{y_{1} + 4}{2} \bigg) \\ \\ \implies \sf 2 = \frac{x_{1} + 1 }{2} \\ \\ \implies \sf \: 4 = x_1 + 1 \\ \\ \implies \sf \: 4 - 1 = x_1 \\ \\ \implies \boxed{\sf \: 3 = x_1}$

Similarly,

$\: \implies \sf \: - 3 = \frac{y_1 + 4}{2} \\ \\ \implies \sf \: - 6 = y_1 + 4 \\ \\ \implies \sf \: - 6 - 4 = y_1 \\ \\ \implies \boxed{ \sf y_1 = - 10}$

Therefore, the co - ordinates of point A are ( 3 , - 10).

Answer 2

Given:

• AB is the diameter of a circle whose Centre is (2,-3) and B is (1,4).

To Find:

• The coordinate of a point A.

Solution:

Centre of the circle will be midpoint of AB.

Let the coordinate of A be (x1 , y1).

As we know that,

Midpoint of a line segment joining the point's (x1 , y1) & (x2 , y2) is ;

(x , y) = (x1 + x2/2 , y1 + y2/2)

Where,

• x = 2
• y = -3
• x2 = 1
• y2 = 4

[ Putting values ]

↪(2 , -3) = (x1 + 1/2 , y1 + 4/2)

↪ 2 = x1 + 1/2

↪2 × 2 = x1 + 1

↪4 - 1 = x1

↪ .°. x1 = 3

↪-3 = y1 + 4/2

↪-3 × 2 = y1 + 4

↪-6 - 4 = y1

↪ .°. y1 = -10

Hence,

• The coordinate of point A is (3.-10).