NCERT Class 11 Mathematics Solutions: Chapter 12 –Introduction to Three Dimensional Geometry Miscellaneous Exercise Part 3

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Understanding of Mid point , property, Apollonius and Angle bisector theore

Mid Point , Property, Apollonius and Angle Bisector Theore

Understanding of Mid point , property, Apollonius and Angle bisector theore

1. A point with x-coordinate lies on the line segment joining the points and . Find the coordinates of the point .

[Hint suppose divides in the ratio . The coordinates of the point are given by ]

Answer:

The coordinates of points are given as .

Consider divide line segment in the ratio .

So, by section formula, the coordinates of point are given by

It is given that the x-coordinate of point .

So, the coordinates of point are

2. If be the points , respectively, find the equation of the set of points such that , where is a constant.

Answer:

The coordinates of points are given as respectively.

Consider the coordinates of point be .

On using distance formula, we obtain

Now, if

So, the required equation is