State whether the following statement is true | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

False

Vedclass · Answer

(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 $Q (0,-4)$.

Similar Questions

State whether the following statement is true or false. Justify your answer.
Point $P(5, -3)$ is one of the two points of trisection of the line segment joining the points $A(7, -2)$ and $B(1, -5)$.

If $A(4, 3)$ and $B(8, 9)$,then the midpoint of $\overline{AB}$ is $\ldots \ldots \ldots \ldots .$

State whether the following statement is true or false. Justify your answer.
The points $A(-1, -2)$,$B(4, 3)$,$C(2, 5)$,and $D(-3, 0)$ in that order form a rectangle.

If $P(at^{2}, 2at)$,$Q(\frac{a}{t^{2}}, \frac{-2a}{t})$ and $S(a, 0)$ are three points,show that $\frac{1}{SP} + \frac{1}{SQ}$ is independent of $t$.

The vertices of $\Delta ABC$ are $A(3, 4)$,$B(0, 0)$,and $C(6, 0)$. Then the length of the median $\overline{AD}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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 $Q (0,-4)$.