Question

The line y = 4 divides the join of points (6, 7) and (4, −1) in the ratio ______.

पर्याय

• 3 : 5

• 5 : 3

• 1 : 5

• 5 : 1

Answer 1

The line y = 4 divides the join of points (6, 7) and (4, −1) in the ratio 3 : 5.

Explanation:

Any point on the line \[y = 4\], can be defined as \[(x, 4).\]

Let point \[(x, 4)\] divide line joining \[(6, 7)\] and \[(4, -1)\] in ratio \[k : 1.\]

By section-formula,

\[(x, y) = \left(\frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2}\right)\]

Substituting values we get:

⇒ \[(x, 4) = \left(\frac{k \times 4 + 1 \times 6}{k + 1}, \frac{k \times -1 + 1 \times 7}{k + 1}\right)\]

⇒ \[(x, 4) = \left(\frac{4k + 6}{k + 1}, \frac{-k + 7}{k + 1}\right)\]

⇒ \[4 = \frac{-k + 7}{k + 1}\]

⇒ \[4(k + 1) = -k + 7\]

⇒ \[4k + 4 = -k + 7\]

⇒ \[4k + k = 7 - 4\]

⇒ \[5k = 3\]

⇒ \[k = \frac{3}{5}\]

Substituting value of \[k\] in \[k : 1\], we get:

⇒ \[\frac{3}{5} : 1\]

⇒ 3 : 5