Step 1:

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The vertices of triangle ABC are $\"\"$ , $\"\"$ and $\"\"$ .

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Ortho center: Ortho center of a triangle is the pont of intersection of all the altitudes of the triangle.

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$\"Orthocenter$

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Slope of the line passing through the points $\"\"$ and $\"\"$ is $\"\"$ .

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Find the slope of the side $\"\"$ passing through $\"\"$ and $\"\"$ .

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$\"\"$ .

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Observe the figure , $\"\"$ and $\"\"$ are perpendicular.

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If $\"\"$ and $\"\"$ are the slopes of two perpedicular lines, then $\"\"$ .

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Slope of the altitude $\"\"$ is $\"\"$ .

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Find the line equation of the altitude $\"\"$ .

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Here $\"\"$

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Point-slope form is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Step 2:

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Find the slope of the side $\"\"$ passing through $\"\"$ and $\"\"$ .

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$\"\"$ .

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Observe the figure , $\"\"$ and $\"\"$ are perpendicular.

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Find the line equation of the altitude $\"\"$ . Slope of the altitude $\"\"$ is $\"\"$ .

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Here $\"\"$ .

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Line passing through the points $\"\"$ and $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Solve (1) and (2) to find the orthocenter.

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From (2): $\"\"$ .

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Substitute $\"\"$ in (1) .

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$\"\"$

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Substitute $\"\"$ in $\"\"$

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$\"\"$

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$\"\"$ .

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Ortho center $\"\"$