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The centre of a circle is (-6,4). If one end of the diameter o

Question

The centre of a circle is $(- 6, 4)$ . If one end of the diameter of the circle is at $(- 12, 8)$ , then the other end is at

(- 18, 12)

(- 9, 6)

(- 3, 2)

(0, 0)

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Noah Discussed

The centre of a circle is

(- 6, 4)

. If one end of the diameter of the circle is at

(- 12, 8)

, then the other end is at

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

The centre is the midpont of the line joining the two points of the diameter.

Using Midpoint-formula

(α, β) \equiv (\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})

From above we have

α = - 6, β = 4

Let

x_{1} = x, y_{1} = y

Given

x_{2} = - 12, y_{2} = 8

We have

α = \frac{x _{1} + x _{2}}{2}

and

β = \frac{y _{1} + y _{2}}{2}

x + \frac{( - 12 )}{2} = - 6

\Rightarrow x - 6 = - 6

∴ x = 0

\Rightarrow y + \frac{8}{2} = 4

\Rightarrow y + 4 = 4

∴ y = 0

Hence, the other point is at

(0, 0)

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Question Text	The centre of a circle is $(- 6, 4)$ . If one end of the diameter of the circle is at $(- 12, 8)$ , then the other end is at
Answer Type	Text solution:1
Upvotes	150