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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`
Solution
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
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