Question

Triangle ABC has vertices of A(-6, 7), B (4, -1), and C (-2, -9). What is the length of the median from angle B?

Answer 1

Answer: The length of the median from angle B is 8 units.

Step-by-step explanation: As shown in the attached figure, A(-6, 7), B(4, -1) and C(-2, -9) are the vertices of ΔABC.

We are to find the length of the median BD from angle B to side AC.

Since BD is the median on side AC. So, D will be the mid-point of side AC.

Therefore, the co-ordinates of the point 'D' are

`\left((-6+(-2))/(2),(7+(-9))/(2)\right)=\left((-8)/(2),(-2)/(2)\right)=(-4,-1).`

Now, the length of median BD is equal to the distance between the vertex 'B' and the point 'D'.

Therefore, the length of median BD calculated using distance formula is

`BD=√((-4-4)^2+(-1+1)^2)\\\\\Rightarrow BD=√(64+0)\\\\\Rightarrow BD=√(64)\\\\\Rightarrow BD=8.`

Thus, the length of the median from angle B is 8 units.

Answer 2

Coordinates of the midpoint of AC:
M ( (-6-2) / 2) , ( 7-9 ) /2 ) = ( -4, -1 )
d ( BM ) = √ ( 4 + 4 )² + ( -1+ 1 )²
d ( BM ) = √ 8 ² =√ 64 = 8
The length of the median from angle B is 8.