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Line equation in slope-intercept form $\"\"$ , where $\"\"$ is slope and $\"\"$ is $\"\"$ -intercept.

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The line equation is $\"\"$ .

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Compare it with slope-intercept form $\"\"$ .

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$\"\"$ .

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Another line containing points $\"\"$ and $\"\"$ , $\"\"$ .

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Slope of the line containing two points is $\"\"$ .

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$\"\"$

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$\"\"$ .

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Since perpendicular lines slopes are negative reciprocals to each other, the line $\"\"$ is perpendicular.

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Midpoint of $\"\"$ and $\"\"$ .

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Formula for the midpoint $\"\"$ .

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Midpoint of $\"\"$ and $\"\"$ $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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The equation is satisfied.

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Therefore, the midpoint of $\"\"$ and $\"\"$ lies on the line $\"\"$ .

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The line containing the points $\"\"$ and $\"\"$ , $\"\"$ is perpendicular to $\"\"$ .

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The midpoint of $\"\"$ and $\"\"$ lies on the line $\"\"$ .