The coordinates of one end point of a diameter of a circle are (4, – 1) and the coordinates of the centre of the circle are (1, 3). Find the co-ordinates of the other end of the diameter?
Answers
Answer:
Step-by-step explanation:
=> We are given that one end point of a circle is (4, -1). We are also given that coordinates of the center of the circle are (1, 3).
=> Let us assume that the radius of the circle as r and given endpoint as A and center as O. Let the other endpoint that we need to find be B.
=> As OA and OB are the radius of the circle, we have OA=OB=r.
=> AB is the diameter of the circle. So, we have AB=2r.
=> Let us consider the ratio of OB and AB
= OBAB = r2r = 12
=> It means that B divides O and A in the ratio 1:2 externally.
=> Now let us consider the formula for the coordinates of the point dividing two points (x1,y1) and (x2,y2) in the m:n externally is (mx2−nx1m−n,my2−ny1m−n).
=> Using this formula, we can find the coordinates of B as,
⇒(1(4)−2(1)1−2,1(−1)−2(3)1−2)⇒(4−2−1,−1−6−1)⇒(2−1,−7−1)⇒(1,−8).
Hence, coordinates of the center of the circle is (1,−8).