Question

Find the length of the median through the vertex B of the triangle ABC with vertices A(9,-2) , B(-3,7) and C(-1,10). ​

Answer 1

Given,

The coordinates of the three vertices of triangle ABC are A(9,-2) , B(-3,7) and C(-1,10).

To find,

The length of the median through the vertex B.

Solution,

According to the basic geometry, the median of of a triangle is a straight line which connects a vertex of that triangle to the midpoint of the opposite side of that vertex.

Here, the opposite side of the vertex B is the AC.

So, first of all we need to calculate the co-ordinate of the midpoint of the AC.

Midpoint of AC = (9-1)/2 , (-2+10)/2 = (4,4)

Length of the median = Distance between the midpoint of AC and the vertex B = ✓(4+3)²+(4-7)² = ✓49+9 = ✓58 units

Hence, the length of the median is ✓58 units.