Question

. The coordinates of one end point of a diameter of a cirde is 14-1) and the centre is
(1.-3). Find the other end of the diameter.​

Answer 1

Answer:

$\bold\red{(-12,-5)}$

Step-by-step explanation:

Given,

One end of a diameter is (14,-1)

and

the centre of circle is (1, -3 )

Let,

the other end of diameter be (x, y)

Now,

We know that,

centre is mid point of a diameter.

Also,

If (a,b) and (c, d) are the ends of a line segment, then its mid point is given by,

$\large\bold{( \frac{a + c}{2} ,\frac{b + d}{2} )}$

Therefore,

we get,

$\frac{14 + x}{2} = 1 \\ \\ = > 14 + x = 2 \\ \\ = > x = 2 - 14 \\ \\ = > x = - 12$

and,

$\frac{ - 1 + y}{2} = - 3 \\ \\ = > - 1 + y = - 3 \times 2 \\ \\ = > y - 1 = - 6 \\ \\ = > y = - 6 + 1 \\ \\ = > y = - 5$

Hence,

the other end of diameter is ( -12, -5 )