Question

13. Find the length of the medians of the triangle whose vertices are (1, -1) , (0, 4)
and (-5, 3). 10. Find the points which divide the line segment joining A(-4 ,0) and B (0,6) into four
equal parts.

Answer 1

13. Let D , E and F are the midpoint of BC, CA , AB sides of triangle ABC.
Use section formula to find D , E and F .
Here, A (1,-1) , B(0,4) and C(-5,3)
D is the midpoint of BC
so, D ≡{(0-5)/2 , (4 + 3)/2 }
D ≡ { -5/2, 7/2 }
Similarly, E ≡ {-2 , 1 } and F ≡ {1/2 , 3/2 }

Now, length of median AD = √{(1 + 5/2)² + (-1 - 7/2)²}
= √{49/4 + 81/4} = √{130/4} = √130/2 unit
Length of median BE = √{(-2)² + (4-1)²} = √13 unit
length of median CF = √{(-5-1/2)² + (3 - 3/2)²}
= √{121/4 + 9/4} = √130/2 unit

10. this question is already solved by me see link https://brainly.in/question/4153656