NCERT Class 11 Mathematics Solutions: Chapter 12 –Introduction to Three Dimensional Geometry Miscellaneous Exercise Part 2
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Understanding of Mid-Point and Mid-Segment
Understanding of mid-point and mid-segment
1. If the origin is the centroid of the triangle with vertices , then find the values of
Answer:
The Triangle PQR
The triangle PQR with vertices P(2a,2,6), Q(-4,3b,-10) and R( 8, 14,2c).
It is known that the coordinates of the centroid of the triangle, whose vertices are and , are
So, coordinates of the centroid of
It is given that origin is the centroid of .
So, the respective values of are .
2. Find the coordinates of a point on y-axis which are at a distance of from the point .
Answer:
If a point is on the y-axis, then x-coordinate and the z-coordinate of the point are zero.
Consider be the point on the y-axis at a distance of from point .
Accordingly,
So, the coordinates of the required points are .