Question

A(10,5),B(6,-3) and C(2,1) are the vertices of a triangle ABC .L is the mid-point , AB and M is the mid-point of AC .Write down the coordinates of L and M .Show that LM=BC/2 .

Answer 1

$\textbf{Given:}$

$\text{A(10,5), B(6,-3) and C(2,1)}$

$\text{Since L is the midpoint of AB, the coordinates of L is}\;(frac{10+6}{2},\frac{5-3}{2})$

$\implies\textbf{L is (8,1)}$

$\text{Since M is the midpoint of AB, the coordinates of M is}\;(frac{10+2}{2},\frac{5+1}{2})$

$\implies\textbf{M is (6,3)}$

$\text{Now}$

$BC=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$BC=\sqrt{(6-2)^2+(-3-1)^2}$

$BC=\sqrt{16+16}$

$\bf\;BC=4\sqrt{2}$.........(1)

$LM=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$LM=\sqrt{(8-6)^2+(1-3)^2}$

$LM=\sqrt{4+4}$

$\bf\;LM=2\sqrt{2}$.........(2)

$\text{From (1) and (2), we get}$

$\bf\;LM=\frac{BC}{2}$

Answer 2

Answer:

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