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Find the coordinates of the point Q on the x–axis which lies on the perpendicular bisector of the line segment joining the points A (–5, –2) and B(4, –2). Name the type of triangle formed by the points Q, A and B.
Find the coordinates of the point Q on the x–axis which lies on the perpendicular bisector of the line segment joining the points A (–5, –2) and B(4, –2). Name the type of triangle formed by the points Q, A and B.
CBSE | Class 10 | Coordinate Geometry | Exercise 7.3 | Maths | NCERT Exemplar
Find the coordinates of the point Q on the x–axis which lies on the perpendicular bisector of the line segment joining the points A (–5, –2) and B(4, –2). Name the type of triangle formed by the points Q, A and B.

Solution:

As the point P lies on the perpendicular bisector of AB, point Q is the midpoint of AB .

NCERT Exemplar Class 10 Maths Chapter 7 Ex. 7.3 Question 6

By the formula for midpoint:

$({{x}_{1}}~+\text{ }{{x}_{2}})/2\text{ }=\text{ }\left( -5+4 \right)/2$

$=\text{ }-{\scriptscriptstyle 1\!/\!{ }_2}$

$x\text{ }=\text{ }-{\scriptscriptstyle 1\!/\!{ }_2}$

Provided that, P lies on x axis, therefore y=0

$P\left( x,y \right)=\text{ }\left( -{\scriptscriptstyle 1\!/\!{ }_2}\text{ },\text{ }0 \right)$

As a result, it is an isosceles triangle.

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