State whether the following statements are true or false. Justify your answer. Point $ P(0,2) $ is the point of intersection of $ y $-axis and perpendicular bisector of line segment joining the points $ A(-1,1) $ and $ B(3,3) $.
Point \( P(0,2) \) is the point of intersection of \( y \)-axis and perpendicular bisector of line segment joining the points \( A(-1,1) \) and \( B(3,3) \).
To do:
We have to find whether the given statement is true or false.
Solution:
Let us assume that the given statement is true.
This implies,
The point \( P(0,2) \) lies on \( y \)-axis.
$P(0,2)$ lies on the perpendicular bisector of $AB$
This implies,
$AP=BP$
$AP=\sqrt{(0+1)^{2}+(2-1)^{2}}$
$=\sqrt{2}$
$BP=\sqrt{(0-3)^{2}+(2-3)^{2}}$
$=\sqrt{9+1}$
$=\sqrt{10}$
$A P ≠ B P$
Therefore,
The point $P$ does not lie on the perpendicular bisector of line segment joining the points \( A(-1,1) \) and \( B(3,3) \).