Question

One end of a diameter of a circle with its
centre at (3, 4) is (2, -5). Find the co
ordinates of the other end.
3​

Answer 1

Equation of the given circle is x

2

+y

2

−4x−6y+11=0

Hence the centre of the circle is (2,3).

The coordinate of the point which lies on the circle is (3,4)

Let the coordinates of the point on the other end of the diameter be (x

1

,y

1

)

The coordinate of midpoint of these two points is (2,3)

x

1

=4−3

x

1

=1

2

y

1

+4

=3

y

1

=6−4

y

1

=2

Hence the coordinates of the point on the other end of the diameter is (1,2)

Answer 2

Answer:

so, the ordinates of the other end (4, 13)

Step-by-step explanation:

let coordinates if other end (X, Y)

center is the midpoint of diameter

mid point =

$( \frac{x1 + x2}{2} \: \frac{y1 + y2}{2} )$

(3,4)=( (2+x )/2, ( -5+Y) /2 )

(2+x)/2=3 (-5+y) /2= 4

2+x= 3×2 (-5+y) = 4×2

x = 6-2 Y= 8+5

X=4 Y= 13

so, the ordinates of the other end (4, 13)