Question

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

Answer 1

Step-by-step explanation:

A(x1,y1)

x=3=( x1+1)/2

therefore x1= 6-1=5

y= -4 = (y1+4)/2

therefore y1= -8-4=-12

therefore coordinates of A = A(5, -12)

Answer 2

The coordinates of point A is (5, -12)

We have to find the coordinates of point A where AB is the diameter of a circle whose centre is (3, -4) and B is (1, 4).

∵ AB is diameter of circle. so points A and B lie on the circumference of circle, do they ?

we know, Centre divides the diameter into two equal parts (we say it ‘radius’)

Using midpoint section formula,

$(x,y)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Here, centre, (x , y) = (3, -4) and B = (x₂ , y₂) = (1, 4)

∴ (3, -4) = [(x₁ + 1)/2, (y₁ + 4)/2]

⇒3 = (x₁ + 1)/2

⇒x₁ = 5

again, -4 = (y₁ + 4)/2

⇒y₁ = -12

therefore the coordinates of A is (5, -12).