Question

From the figure given alongside, find the length of the median AD of triangle ABC. Complete the activity.

Solution:

Here A(–1, 1), B(5, – 3), C(3, 5) and suppose D(x, y) are coordinates of point D.

Using midpoint formula,

x = `(5 + 3)/2`

∴ x = `square`

y = `(-3 + 5)/2`

∴ y = `square`

Using distance formula,

∴ AD = `sqrt((4 - square)^2 + (1 - 1)^2`

∴ AD = `sqrt((square)^2 + (0)^2`

∴ AD = `sqrt(square)`

∴ The length of median AD = `square`

Answer 1

Here A(–1, 1), B(5, – 3), C(3, 5) and suppose D(x, y) are coordinates of point D. D is the midpoint of seg BC.

Using midpoint formula,

x = `(x_1 + x_2)/2`

x = `(5 + 3)/2`

∴ x = `8/2`

∴ x = 4

y = `(y_1 + y_2)/2`

y = `(-3 + 5)/2`

∴ y = `2/2`

∴ y = 1

Using distance formula,

∴ AD = `sqrt((4 - (-1))^2 + (1 - 1)^2`

∴ AD = `sqrt((5)^2 + (0)^2`

∴ AD = `sqrt(25)`

∴ The length of median AD = 5 cm