Coordinate Geometry (Hard)

Coordinate Geometry: core idea

• 1. A circle through $(1,2),(7,2),(4,6)$ has center $(4,k)$. Find $k$.

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• 2. The line through $(1,5),(5,1)$ meets $y=2$ at $(a,2)$. Find $a$.

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• 3. A square has adjacent vertices $(1,1),(5,4)$. Find its area.

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• 4. Find the distance from $(4,-3)$ to $3x+4y=0$.

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• 5. The perpendicular bisector of $(2,1),(8,5)$ meets $y=0$ at $(a,0)$. Find $a$.

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• 6. A line of slope $-2$ through $(3,7)$ meets the $x$-axis at $(a,0)$. Find $a$.

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• 7. Find the area of $(0,0),(6,0),(8,3),(2,3)$.

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• 8. Lines $x+y=8$ and $2x-y=1$ meet at $(a,b)$. Find $ab$.

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• 9. A circle centered at $(3,-1)$ is tangent to the $y$-axis. Find area$/\pi$.

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