Q19 of 48 Page 102

Find the length of medians of the triangle whose vertices are (1, –1), (0, 4) and (–5, 3).

We have the vertices of ∆ABC, A (1, –1), B (0, 4) and C (–5, 3).


Let D, E and F be the mid points of the sides BC, CA and AB respectively.



Using the mid–point formula,


Coordinates of D are


Coordinates of E are = (–2, 1)


Coordinates of F are


Using distance formula,


Length of median AD =


=


=


=


=


=



Length of median BE =


=


=


=


Length of median CF =


=


=


=


=


=


∴ The lengths of medians of the triangle whose vertices are (1, –1), (0, 4) and (–5, 3) are and √13.


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 18

Prove that the mid–point C of the hypotenuse in a right angled triangle AOB is situated at equal distances from the vertices O, A and B of the triangle.

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Prove that the mid–point of the line segment joining the points (5, 7) and (3, 9) is the same as the mid–point the line segment joining the points (8, 6) and (0, 10).

 21

If the mid–points of the sides of a triangle are (1, 2), (0, –1) and (2, –1), then find the coordinates of the vertices of the triangle.