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

If the centroid of $\Delta ABC$ is $G(3, 3)$ and the vertices are $B(-1, 2)$ and $C(2, -3)$,then find the area of $\Delta ABC$.

If $A(0, 0)$,$B(2, 0)$,$C(2, 2)$,and $D(0, 2)$,then $\square ABCD$ is a $\ldots \ldots \ldots$

If $D\left(\frac{-1}{2}, \frac{5}{2}\right)$,$E(7, 3)$,and $F\left(\frac{7}{2}, \frac{7}{2}\right)$ are the midpoints of the sides of $\triangle ABC$,find the area of $\triangle ABC$.

In $\Delta ABC,$ if $A(0, 0), B(4, 0)$ and $C(0, 3)$ then $\Delta ABC$ is a $\ldots \ldots \ldots$ triangle.

The segment joining $A (-2, 1)$ and $B (7, 8)$ is divided into five congruent segments. Find the coordinates of the third point from $A$.

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 $Q (0,-4)$.