Question

If A(-1, 3), B(1, - 1) and C(5, 1) are the vertices of the triangle ABC, then find the length of the median from B to side AC. (A) 18
(B) 213
(C) 110
(D) 8​

Answer 1

Answer:

median of a triangle is a line segment that joins the vertex of a triangle to

the midpoint of the opposite side.

Median through A passed through mid point of BC.

Mid point of two points (x

1

,y

1

) and (x

2

,y

2

) is calculated by the formula (

2

x

1

+x

2

,

2

y

1

+y

2

)

Using this formula,

mid point of BC =(

2

1+5

,

2

−1+1

)=(3,0)

Distance between two points (x

1

,y

1

) and (x

2

,y

2

) can be calculated using the formula

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

Length of median through A =

(3+1)

2

+(0−3)

2

=

16+9

=

25

=5units

Answer 2

Answer:

$\sqrt{10}$

Step-by-step explanation:

A median of a triangle is a line segment that joins the vertex of a triangle to the midpoint of the opposite side.

Median through B passed through midpoint of AC.

The two midpoints are

$(x _{1} y_{1}) \: and \: ( x_{2} y_{2})$

The midpoints of AC is calculated as :

$(\frac{x_{1} + x_{2} } {2}, \frac{y_{1} + y_{2} } {2}) = (\frac{-1 + 5} {2} , \frac{3 + 1} {2} ) = (2,2)$

Distance between two points (x1, y1) and (x2, y2) can be calculated using the

$\sqrt{( x_{2} - x_{1})^{2} + (y_{2} - y _{1})} = \\ \sqrt{(2 - {1}^{2}) + (2 + {1}^{2}) } = \sqrt{10}$

The length of the median from B to side AC is

$\sqrt{10}$