# Find the lengths

Given: The vertices of the triangle are A (0, 0, 6), B (0, 4, 0) and C (6, 0, 0).

x1 = 0, y1 = 0, z1 = 6; x2 = 0, y2 = 4, z2 = 0; x3 = 6, y3 = 0, z3 = 0 We know that the median is a line segment through a vertex of a triangle to the midpoint of the side opposite to the vertex.

So, let the medians of this triangle be AD, BE and CF corresponding to the vertices A, B and C respectively.

D, E and F are the midpoints of the sides BC, AC and AB respectively.

By Midpoint Formula, we know that the coordinates of the mid-point of the line segment joining two points P (x1, y1, z1) and Q (x2, y2, z2) are .

So, we have

The coordinates of D = (3, 2, 0)

The coordinates of E = (3, 0, 3)

And the coordinates of F = (0, 2, 3)

By Distance Formula, we know that the distance between two points P (x1, y1, z1) and Q (x2, y2, z2) is given by .

The lengths of the medians are:   So, the lengths of the medians of the given triangle are 7, and 7.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Determine the poiRD Sharma - Mathematics

Let (3, 4, -1) anRD Sharma - Mathematics

The length of theRD Sharma - Mathematics

If P (0, 1, 2), QRD Sharma - Mathematics

Show that the triMathematics - Exemplar

Write the length RD Sharma - Mathematics

If the distance bRD Sharma - Mathematics

Find the point onRD Sharma - Mathematics

Find the point onRD Sharma - Mathematics

Write the coordinRD Sharma - Mathematics