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 = \[\boxed{4}\]

`y = (y_1 + y_2)/2`

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

∴ `y = 2/2`

∴ y = \[\boxed{1}\]

Using distance formula,

∴ AD = \[\sqrt{(4 - \boxed{-1})^2 + (1 - 1)^2}\]

∴ AD = \[\sqrt{(\boxed{5})^2 + (0)^2}\]

∴ AD = \[\sqrt{\boxed{25}}\]

∴ The length of median AD = \[\boxed{5 \phantom{.}\text{cm}}\]