Question

Seg AB is a diameter of a circle with centre P (1,2). If A (-4,2), then find the co-ordinates of point ​

Answer 1

Given info : Segment AB is a diameter of a circle with centre P(1,2).

To find : if point A(-4,2), then find the coordinate of point B.

solution : A(-4,2) --------- P(1,2) ---------- B

we know, Centre of circle is the midpoint of diameter.

using midpoint section formula,

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

here, (x , y) = (1, 2) , (x₁ , y₁) = (-4, 2) and B = (x₂ , y₂) = ?

so, (1, 2) = [(-4 + x₂)/2, (2 + y₂)/2 ]

⇒1 = (-4 + x₂)/2

⇒x₂ = 6

2 = (2 + y₂)/2

⇒y₂ = 4 - 2 = 2

therefore coordinates of point B (6, 2).