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प्रश्न
Write down the equation of the line whose gradient is `-2/5` and which passes through point P, where P divides the line segement joining A(4, −8) and B(12, 0) in the ratio 3 : 1.
उत्तर
Given, P divides the line segment joining A(4, −8) and B(12, 0) in the ratio 3 : 1.
Co-ordinates of point P are
`((3 xx 12 + 1 xx 4)/(3 + 1),(3 xx 0 + 1 xx (-8))/(3 + 1))`
= `((36 + 4)/4, (0 - 8)/4)`
= `(40/4, (-8)/4)`
= (10, −2)
Slope = m = `(-2)/5` ...(Given)
Thus, the required equation of the line is
y − y1 = m(x − x1)
`y + 2 =(-2)/5 (x - 10)`
5y + 10 = −2x + 20
2x + 5y = 10
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