Question

State whether the following statement is true or false.

Enter $1$ for true and $0$ for false

Point P (0, 2) is the point of intersection of the y-axis and the perpendicular bisector of the line segment joining the points A (1, 1) and B (3, 3).

Answer 1

$ThepointP(x,y)=(0,2)liesontheperpendicularbisectorofaline$

$segmentABwhentheco-ordinatesofA\&BareA(x_1,y_1)=(1,1)and$

$B(x_2,y_2)=(3,3).$

$SoAPshouldbe=BP.$

$NowAP=\sqrt{{(x_1-x)}^2+{(y_1-y)}^2}=\sqrt{{(1-0)}^2+{(1-2)}^2}units=\sqrt{2}unitsand$

$BP=\sqrt{{(x_2-x)}^2+{(y_2-y)}^2}=\sqrt{{(3-0)}^2+{(3-2)}^2}units=\sqrt{10}units.$

$\therefore AP\ne BPi.eP(0,2)doesnotlieontheperpendicularbisector$

$ofthelinesegmentAB.$

$Sothestatementisfalse.$

$Ans-FALSE.$