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Find the lengths of the medians of a ABC whose vertices are A

Question

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

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Find the lengths of the medians of a

Δ A BC

whose vertices are

A (0, - 1)

B (2, 1)

and

C (0, 3)

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Given: Vertices of

Δ A BC

are

A (0, - 1), B (2, 1)

and

C (0, 3)

Let AD, BE and CF are the medians of sides BC, CA and AB respectively, then

Step

1

: Find Coordinates of D, E and F

Coordinates of D:

= (\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})

= (\frac{2 + 0}{2}, \frac{1 + 3}{2})

= (\frac{2}{2}, \frac{4}{2}) = (1, 2)

Coordinates of E:

(0, \frac{2}{2}) = (0, 1)

Coordinates of F:

(\frac{2}{2}, 0) = (1, 0)

Step

2

: Find the length of AD, BE and CF

Using

Distance formula

= (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

Length of AD

= (1 - 0)^{2} + (2 + 1)^{2} = 1^{2} + 3^{2}

= 1 + 9 = 10

units

Length of BE

= (2 - 0)^{2} + (1 - 1)^{2}

= 2^{2} + (0)^{2}

= 2

units

Length of CF

= (1 - 0)^{2} + (0 - 3)^{2}

= 1 + 9 = 10

units.

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Question Text	Find the lengths of the medians of a $Δ A BC$ whose vertices are $A (0, - 1)$ , $B (2, 1)$ and $C (0, 3)$ .
Answer Type	Text solution:1
Upvotes	150

Find the lengths of the medians of a ΔABC whose vertices are A(0,−1), B(2,1) and C(0,3).

Text solutionVerified

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