Question

the coordinates of the centre of a circle are (-3,1.5) if the ends of a diameter are -3,y) and (x,-2) . find X and Y


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Answer 1

Answer:

Given –

• The coordinates of the centre of the circle : (-3, 1.5) ➜ (x, y).
• The coordinates of one end of the diameter : (-3, y) ➜ (x1, y1).
• The coordinates of other end of the diameter : (x, -2) ➜ (x2, y2).

To Find –

• X and Y ?

Solution –

The centre of the circle is the midpoint of the diameter, hence we will use the midpoint formula.

Midpoint Formula : (x, y) = (x1 + x2)/2, (y1 + y2)/2.

For Finding x first,

➸ -3 = (x1 + x2)/2

➸ -3 = (-3 + x)/2

➸ -3 * 2 = -3 + x

➸ -6 = -3 + x

➸ -6 + 3 = x

➸ x = -3

For Finding y,

➸ 1.5 = (y1 + y2)/2

➸ 1.5 = (y + -2)/2

➸ 1.5 * 2 = y - 2

➸ 3.0 = y - 2

➸ y = 3 + 2

➸ y = 5

Hence, x = -3 and y = 5.

Answer 2

Given:

• The coordinates of the center of the circle: (-3, 1.5).
• The coordinates of the ends of the diameter: (-3, y) and (x, -2).

To find: The values of x and y.

Answer:

Since the coordinates of the centre of the circle is given, we'll use the mid-point formula.

Mid-point formula:

$\tt Mid-point\ =\ \Bigg(\dfrac{x_1\ +\ x_2}{2},\ \dfrac{y_1\ +\ y_2}{2}\Bigg)$

From the given points, we have:

$\tt Mid - point\ =\ (-3,\ 1.5)\\\\x_1\ =\ -3\\\\x_2\ =\ x\\\\y_1\ =\ y\\\\y_2\ =\ -2$

Using them in the formula,

$\tt \Bigg(-3,\ 1.5\Bigg)\ =\ \Bigg(\dfrac{-3\ +\ x}{2},\ \dfrac{y\ -\ 2}{2}\Bigg)$

Equating the x coordinates,

$\tt -3\ =\ \dfrac{-3\ +\ x}{2}\\\\\\-6\ =\ -3\ +\ x\\\\\\-6\ +\ 3\ =\ x\\\\\\\bf-3\ =\ x$

Equating the y coordinates,

$\tt 1.5\ =\ \dfrac{y\ -\ 2}{2}\\\\\\3\ =\ y\ -\ 2\\\\\\3\ +\ 2\ =\ y\\\\\\\bf 5\ =\ y$

Therefore, the values of x and y are -3 and 5.