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{{ printedBook.courseTrack.name }} {{ printedBook.name }} In the diagram, we can see that $M$ is the midpoint of $AC$ and that $BD$ is the perpendicular to $AC$ through $M.$ Therefore, $BD$ is the perpendicular bisector of $AC.$

According to the Perpendicular Bisector Theorem, in a plane, if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. In our case, $D,$ is the point on the perpendicular bisector and $A$ and $C$ are the endpoints. Therefore, according to the theorem, $AD=CD.$

Since $AD=CD,$ we can write an equation to find $x.$ $AD=CD⇒9x+1=7x+10 $ Let's solve the equation for $x.$$9x+1=7x+10$

$x=4.5$