Question

If the centre of the circle is (3, -4) and one end of the diameter is (1, 4) then the coordinates of other end

Answer 1

Answer:-

Given,

• O (3,-4) is the centre of a circle.
• A (1,4) is the one end of the diameter.

To Find,

• The coordinates of the other end of the diameter.

Formula,

• $\tt{\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}}$

Solution,

$\tt\underline{\bf{\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}}}$

$\leadsto\sf{(\dfrac{x_1+1}{2}=3),(\dfrac{y_1+4}{2}=-4)}$

$\leadsto\sf{(x_1+1=6),(y_1+4=-8)}$

$\leadsto\sf{(x_1=6-1),(y_1=-8-4)}$

$\leadsto\sf{(x_1=5),(y_1=-12)}$

Hence, the points B (5, -12).

Concept used,

The diameter is given and one of the coordinates of one end of the diameter along with the coordinates of the centre of the circle is given.

The other end of the diameter can you simply found out using the midpoint formula.

This is because, centre of the circle is the midpoint of the diameter.