Question

Find the lengths of the medians of a Triangle ABC having vertices at A(0, -1), B (2,1) and C (0,3).

Answer 1

Given :

• Vertices of triangle : A(0, -1), B (2,1) and C (0,3)

To find :

• Length of medians of triangle ABC

Concept used :

• Median of triangle drawn from a vertex divides it's opposite side in equal parts.

• Distance Formula :- √[(x2-x1)²+(y2-y1)²]

Solution :

Vertices of triangle are given as :- A(0, -1), B (2,1) and C (0,3) .

In the given diagram ( refer attachment) :

AD is median on BC and D is midpoint of BC.

⟹ Therefore co-ordinates of point D = (2+0)/2 , (1+3)/2

⟹ co-ordinates of point D = ( 2/2 , 4/2 )

⟹ co-ordinates of point D = ( 1 , 2 )

Now we will apply distance formula to find length of Median AD .

⟹ length of Median AD = √[(1-0)²+(2+1)²]

⟹ length of Median AD = √10 units

BE is median on AC and E is midpoint of AC.

⟹ Therefore co-ordinates of point E = (0+0)/2 , (-1+3)/2

⟹ co-ordinates of point E = ( 0 , 2/2)

⟹ co-ordinates of point E = ( 0 , 1)

Now we will apply distance formula to find length of Median BE.

⟹ length of Median BE = √[(0-2)²+(1-1)²]

⟹ length of Median BE = √(4+0)

⟹ length of Median BE = √4

⟹ length of Median BE = 2 units

FC is median on AB and E is midpoint of AC.

⟹ Therefore co-ordinates of point F = (0+2)/2 , (-1+1)/2

⟹ co-ordinates of point F = (2/2 , 0/2)

⟹ co-ordinates of point F =( 1 , 0)

Now we will apply distance formula to find length of Median CF.

⟹ length of Median CF = √[(0-1)²+(3-0)²]

⟹ length of Median CF = √(1+9)

⟹ length of Median CF = √10

⟹ length of Median CF = √10 units

Answer :

• length of Median AD = √10 units
• length of Median BE = 2 units
• length of Median CF = √10 units