ABC is a triangle, whose vertices are A(2, -4), B(-2, 1) and C(6, -6). Find its centroid and the length of the median through A.
[4 MARKS]

Open in App

Solution

Formula: 1 Mark each
Coordinates of centroid: 1 Mark
Length of median: 1 Mark

Coordinates of centroid G
$= (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$
$= (\frac{2 - 2 + 6}{3}, \frac{- 4 + 1 - 6}{3}) = (2, - 3)$
Mid - point D of BC $= (\frac{- 2 + 6}{2}, \frac{1 - 6}{2}) = (2, - \frac{5}{2})$
$∴$ Length of median $A D = \sqrt{(2 - 2)^{2} + {(\frac{- 5}{2} + 4)}^{2}}$
$= \frac{3}{2} u n i t s$

Suggest Corrections

Similar questions

Find the lengths of the medians of a triangle ABC whose vertices are A(7, –3), B(5, 3) and C(3, –1). [4 MARKS]

If A (5, –1), B(–3, –2) and C(–1, 8) are the vertices of triangle ABC, find the length of median through A and the coordinates of the centroid.

△ A B C

A (- 1, 2), B (2, 1)

C (0, 4)

△ A B C

Find the lengths of the medians of a $△ A B C$ whose vertices are A(0,-1), B(2,1) and C(0, 3)

Join BYJU'S Learning Program