Point P (0, –7) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A (–1, 0) and B (7, –6). Is the following statement true or false
Solution:
We know that
Points which lie on the perpendicular bisector of the line segment which joins the two points is equidistant from the two points
It means that PA should be equal to PB
The distance between two points (x₁, y₁) and (x₂, y₂) is
d=\(\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)
Let us consider
PA = \(\sqrt{(-1-0)^{2}+(0+7)^{2}}=\sqrt{1+49}=\sqrt{50}\)
PB = \(\sqrt{(7-0)^{2}+(-6+7)^{2}}=\sqrt{49+1}=\sqrt{50}\)
As PA = PB, the given statement is true.
Therefore, point P (0, -7) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A (-1, 0) and B (7, -6).
✦ Try This: 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).
We know that
Points which lie on the perpendicular bisector of the line segment which joins the two points is equidistant from the two points
It means that PA should be equal to PB
The distance between two points (x₁, y₁) and (x₂, y₂) is
d=\(\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)
Let us consider
PA = \(\sqrt{(-1-0)^{2}+(0-2)^{2}}=\sqrt{1+4}=\sqrt{5}\)
PB = \(\sqrt{(3-0)^{2}+(3+2)^{2}}=\sqrt{9+25}=\sqrt{34}\)
As PA ≠ PB, the given statement is false.
Therefore, point P (0, 2) is not the point of intersection of the y-axis and perpendicular bisector of the line segment joining the points A (-1, 1) and B (3, 3).
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7
NCERT Exemplar Class 10 Maths Exercise 7.2 Sample Problem 3
Point P (0, –7) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A (–1, 0) and B (7, –6). Is the following statement true or false
Summary:
Point P (0, –7) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A (–1, 0) and B (7, –6) is true
☛ Related Questions:
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