Question

3. Find the length of median AD of the
triangle formed by the points A(0,6), B(8,0)
and C(4,2).
(2)

Answer 1

Step-by-step explanation:

D is the mid point of CB

So coordinate of D = (6,1)

Now by using distance formula ans = root 36 + 25 = root 61

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Answer 2

$\huge\tt{\underline{\underline{Given:-}}}$

• Coordinates of vertices of ΔABC are A(0,6) , B(8,0) and C (4,2)

$\huge\tt{\underline{\underline{To\:Find:-}}}$

• Length of median AD

$\huge\tt{\underline{\underline{Solution:-}}}$

★ Median is the line segment which joins the opposite vertex and the mid point of the opposite side.

Median AD bisects the side BC of the triangle . So the mid point of B and C is D .

Let coordinates of D be (x,y)

Midpoint of line segment (x,y) joining the points (x₁ , y₁) and (x₂ , y₂) is given by ,

${ \underline { \boxed{ \bold{ { \bigstar \: (x,y) =\bigg(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\bigg)}}}}}$

By comparing the coordinates of B and C vertices we get ,

• x₁ = 8 , x₂ = 4
• y₁ = 0 , y₂ = 2

$\large\rm{\implies{(x,y)\:=\:\bigg(\frac{8+4}{2},\frac{0+2}{2}\bigg)}}$

$\large\rm{\implies{(x,y)\:=\:\bigg(\frac{12}{2},\frac{2}{2}\bigg)}}$

$\large\rm{\implies{(x,y)\:=\:(6,1)}}$

Distance between A and D is equal to the length of median AD ,

Distance between any two points (x₁ , y₁ ) and (x₂ , y₂ ) is given by ,

${ \underline{ \boxed{ \bold{ { \bigstar\:D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}}}}}$

By comparing the coordinates of vertices of A and D we get ,

• x₂ = 6 , x₁ = 0
• y₂ = 1 , y₁ = 6

$\implies \: d \: = \sqrt{(6 - 0) {}^{2} + (1 - 6) {}^{2} } \\ \\ \implies \: d = \sqrt{36 + 25} = \sqrt{61}$

$\large{\bold{\dag{\:Hence , The \ length \ of \ AD \ is \ \sqrt{61}}}} \\ \large{\bold{units}}$