If the midpoint of the line segment joining the points (-7, 14) and (k, 4) is (a, b) where 2a + 3b = 5. Find the value of k.

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k = -15

k = -1

None of these

k = 5

answer is A.

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Detailed Solution

Given that, (a,b) is the midpoint of (-7,14) & (k,4) and 2a + 3b = 5.
We need to find the value of k.
Midpoint of two points

(x_{1}, y_{1})

and

(x_{2}, y_{2})

is calculated by the formula,

(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

So, the midpoint of

(- 7, 14), (k, 4) = (a, b)

\Rightarrow (\frac{- 7 + k}{2}, \frac{14 + 4}{2}) = (a, b)

Equating x and y-coordinates, we get,

\Rightarrow a = \frac{- 7 + k}{2} and b = 9

\Rightarrow 2 a + 3 b = 5

(Given)

\Rightarrow 2 \times \frac{- 7 + k}{2} + 3 (9) = 5

\Rightarrow - 7 + k + 27 = 5

\Rightarrow k = - 15

Thus, the value of k is -15.
Therefore, option (1) is correct.

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