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(B) False.If a point $A$ lies on the perpendicular bisector of a line segment $PQ$,then it must be equidistant from the endpoints $P$ and $Q$,i.e.,$AP

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False

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(B) False.If a point $A$ lies on the perpendicular bisector of a line segment $PQ$,then it must be equidistant from the endpoints $P$ and $Q$,i.e.,$AP = AQ$.First,calculate the distance $AP$ using the distance formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$:$AP = \sqrt{(6-2)^2 + (5-7)^2} = \sqrt{4^2 + (-2)^2} = \sqrt{16 + 4} = \sqrt{20}$.Next,calculate the distance $AQ$:$AQ = \sqrt{(0-2)^2 + (-4-7)^2} = \sqrt{(-2)^2 + (-11)^2} = \sqrt{4 + 121} = \sqrt{125}$.Since $AP 
eq AQ$ (as $\sqrt{20} 
eq \sqrt{125}$),the point $A (2,7)$ does not lie on the perpendicular bisector of the line segment $PQ$.

State whether the following statement is true or false. Justify your answer.
The point $A (2,7)$ lies on the perpendicular bisector of the line segment joining the points $P (6,5)$ and $Q (0,-4)$.

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State whether the following statement is true or false. Justify your answer.The point $A (2,7)$ lies on the perpendicular bisector of the line segment joining the points $P (6,5)$ and $Q (0,-4)$.