Question

Find the ratio in which the YZ-plane divides the line segment formed by joining
the points (-2.4.7) and (3.-5. 8)​

Answer 1

SOLUTION

TO DETERMINE

The ratio in which the YZ-plane divides the line segment formed by joining the points (-2, 4, 7) and (3, -5, 8)

EVALUATION

Let n : m be the required ratio

So the point where the line segment formed by joining the points (-2, 4, 7) and (3, -5, 8) is

$\displaystyle \sf{ \bigg( \: \frac{ - 2m + 3n}{m + n}, \frac{ 4m - 5n}{m + n}, \frac{ 7m + 8n}{m + n} \bigg)}$

Now the line segment is divided by YZ plane

∴ x - component = 0

$\displaystyle \sf { \implies \: \frac{ - 2m + 3n}{m + n} = 0 }$

$\displaystyle \sf { \implies \: - 2m + 3n = 0 }$

$\displaystyle \sf { \implies \: 2m = 3n }$

$\displaystyle \sf { \implies \: \frac{n}{m} = \frac{2}{3} }$

$\displaystyle \sf { \implies \: n : m = 2 : 3}$

Hence the line segment formed by joining the points (-2, 4, 7) and (3, -5, 8) is divided by YZ plane in ratio 2 : 3 internally

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