Question

6. One end of a diameter of a circle is at (2,3) and the centre is (-2,5), what are the co-ordinates of the

other end of this diameter.​

Answer 1

Solution :-

Let the coordinates of diameter be A(2,3) B(x,y)

Centre of the circle be M(-2,5)

We know that

Centre of a circle divides the diameter into 2 equal parts.

So, centre of the circle is the mid point of the diameter

Using Mid point formula

$M(x, y) = \bigg( \dfrac{x_1 +x_2}{2} , \dfrac{y_1 + y_2 }{2} \bigg)$

A(2,3) B(x,y) M(-2,5)

Here,

• x1 = 2
• y1 = 3
• x2 = x
• y2 = y

Substituting the values

$\implies M( - 2, 5) = \bigg( \dfrac{2 +x}{2} , \dfrac{3+ y}{2} \bigg)$

Comparing x coordinates

$\implies - 2 = \dfrac{2 +x}{2}$

$\implies - 4 =2 +x$

$\implies x = - 4 - 2 = - 6$

Comparing y coordinates

$\implies 5 = \dfrac{3+ y}{2}$

$\implies 10= 3+ y$

$\implies y= 10 - 3 = 7$

Therefore the coordinates of the other end is (-6,7).

Answer 2

Answer:

$\large\boxed{\sf{(-6,7)}}$

Step-by-step explanation:

One end of diameter = (2,3)

Centre of circle = (-2,5)

Also, the centre of Circle is the centre of the diameter.

.°. Centre of diameter = (-2,5)

Let, the other end of diameter = (x,y)

Now, by mid point section formula :

$= > \frac{2 + x}{2} = - 2 \\ \\ = > 2 + x = - 2 \times 2 \\ \\ = > x = - 4 - 2 \\ \\ = > x = - 6$

And

$= > \frac{3 + y}{2} = 5 \\ \\ = > 3 + y = 5 \times 2 \\ \\ = > y = 10 - 3 \\ \\ = > y = 7$

Hence, other end of diameter is (-6,7)