Given:

The vertices of a triangle are A (1, 2, 3), B (0, 4, 1), C (-1, -1, -3)

By using the distance formula,

The distance between A(1, 2, 3) and B (0, 4, 1) is AB

\( \sqrt{(1-0)^2+(2-4)^2+(3-1)^2}\)

\( \sqrt{9}=3\)

The distance between A(1, 2, 3) and C(-1, -1, -3) is AC

\( \sqrt{(1-(-1))^2+(2-(-1))^2+(3-(-3))^2}\)

\( \sqrt{49}=7\)

So, \( \dfrac{AB}{AC}\) = \( \dfrac{3}{7}\)

AB: AC = 3:7

BD: DC = 3:7

Then, m = 3 and n = 7

B(0, 4, 1) and C(-1, -1, -3)

Coordinates of D by using section formula is given as

The coordinates of D are (\( \dfrac{-3}{10}\), \( \dfrac{5}{2}\), \( \dfrac{-1}{5}\)).

Answered by Aaryan | 9 months agoThe mid-points of the sides of a triangle ABC are given by (-2, 3, 5), (4, -1, 7) and (6, 5, 3). Find the coordinates of A, B and C.

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