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Standard X

Mathematics

Mid Point

A2,3,7, B -1,...

Question

A(2,3,7), B (-1,3,2) and C (p,5,r) are vertices of a triangle. If the median through A is equally inclined to the co-ordinate axes then find the co-ordinates of the midpoint of BC in terms of p and r.

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Solution

Here $A \equiv (2, 3, 7) B \equiv (- 1, 3, 2) C \equiv (p, 5, r)$
Let the mid point of BC is D.
$∴$ D has coordinates = $(\frac{p - 1}{2}, \frac{5 + 3}{2}, \frac{r + 2}{2})$
= $(\frac{p - 1}{2}, 4, \frac{r + 2}{2})$

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A(2,3,7), B (-1,3,2) and C (p,5,r) are vertices of a triangle. If the median through A is equally inclined to the co-ordinate axes then find the co-ordinates of the midpoint of BC in terms of p and r.

Here A≡(2,3,7)B≡(−1,3,2)C≡(p,5,r)Let the mid point of BC is D. ∴ D has coordinates =(p−12,5+32,r+22) =(p−12,4,r+22)

Here $A \equiv (2, 3, 7) B \equiv (- 1, 3, 2) C \equiv (p, 5, r)$
Let the mid point of BC is D.
$∴$ D has coordinates = $(\frac{p - 1}{2}, \frac{5 + 3}{2}, \frac{r + 2}{2})$
= $(\frac{p - 1}{2}, 4, \frac{r + 2}{2})$