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Question
In what ratio does the x-axis divide the line segment joining the points (– 4, – 6) and (–1, 7)? Find the coordinates of the point of division.
Solution
Let the ratio in which x-axis divides the line segment joining (– 4, – 6) and (–1, 7) = 1 : k
Then,
x-coordinate becomes `(-1 - 4k)/(k + 1)`
y-coordinate becomes `(7 - 6k)/(k + 1)`
Since P lies on x-axis, y coordinate = 0
`(7 - 6k)/(k + 1)` = 0
7 – 6k = 0
k = `6/7`
Now, m1 = 6 and m2 = 7
By using section formula,
x = `(m_1x_2 + m_2x_1)/(m_1 + m_2)`
= `(6(-1) + 7(-4))/(6 + 7)`
= `(-6 - 28)/13`
= `(-34)/13`
So, now
y = `(6(7) + 7(-6))/(6 + 7)`
= `(42 - 42)/13`
= 0
Hence, the coordinates of P are `((-34)/13, 0)`
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