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Mathematics

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

Coordinate Geometry

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Answer

Let coordinates of A be (x, y) and C be the center (2, -3).

Find the coordinates of a point A, where AB is the diameter of a circle whose center is (2, -3) and B is (1, 4). NCERT Class 10 Mathematics CBSE Solutions.

Given,

B = (1, 4).

We know that,

Center is the mid-point of diameter.

By formula,

Mid-point = (x1+x22,y1+y22)\Big(\dfrac{x1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

Substituting values we get :

⇒(2,−3)=(x+12,y+42)⇒2=x+12,−3=y+42⇒x+1=4,y+4=−6⇒x=4−1=3,y=−6−4=−10.\Rightarrow (2, -3) = \Big(\dfrac{x + 1}{2}, \dfrac{y + 4}{2}\Big) \\[1em] \Rightarrow 2 = \dfrac{x + 1}{2}, -3 = \dfrac{y + 4}{2} \\[1em] \Rightarrow x + 1 = 4, y + 4 = -6 \\[1em] \Rightarrow x = 4 - 1 = 3, y = -6 - 4 = -10.

A = (x, y) = (3, -10).

Hence, co-ordinates of A = (3, -10).

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