$\"\"$

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The line equations are $\"\"$ and $\"\"$ .

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Graph :

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Graph the line equations $\"\"$ and $\"\"$ .

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$\"\"$

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Observe the graph :

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Point of intersection are $\"\"$ and $\"\"$ .

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Find the mid point of the system.

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Mid point : $\"\"$ .

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Mid point of the points $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ .

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Mid point of the points $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ .

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Mid point of the points $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ .

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The mid point of the systems are $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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Find the perpendicular bisectors.

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Perpendicular bisectors are the lines equation that are perpendicular to the given line equation.

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1.

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The line equation is $\"\"$ .

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$\"\"$

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

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Slope of the perpendicular bisector is $\"\"$ .

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The equation of perpendicular bisectors are in the form of $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the $\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in the perpendicular bisector equation.

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Perpendicular bisector equation is $\"\"$ .

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2.

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The line equation is $\"\"$ .

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$\"\"$

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

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Slope of the perpendicular bisector is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the $\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in the perpendicular bisector equation.

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Perpendicular bisector equation is $\"\"$ .

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3.

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The function $\"\"$ .

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$\"\"$

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

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Slope of the perpendicular bisector is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the $\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in the perpendicular bisector equation.

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Perpendicular bisector equation is $\"\"$ .

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Graph :

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Graph the equations $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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Observe the graph :

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The three lines intersects at $\"\"$ .

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The point $\"\"$ is the center of the circle.

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$\"\"$

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The radius of the circle is the distance between the point and vertex.

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Vertex $\"\"$ and point is $\"\"$ .

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$\"\"$

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$\"\"$ .

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The standard form of the equation of the circle is $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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Graph :

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Graph the line equations $\"\"$ and $\"\"$ .

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Graph the circle $\"\"$ .

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$\"\"$

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$\"\"$

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The equation of the circle circumference of the triangle $\"\"$ .