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प्रश्न
The line joining the points (2, 1) and (5, −8) is trisected at the points P and Q. If point P lies on the line 2x − y + k = 0. Find the value of k.
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उत्तर
Key concept: Section formula
`(x,y) = (mx_2 +nx_1)/(m+n), (my_2 + ny_1)/(m+n)`
`p(x,y) = (1(5)+2(2))/(1+2), (1(-8)+2(1))/(1+2)`
`x = (5+4)/3`
`x=9/3`
x = 3
`y = (-8+2)/3`
`y = (-6)/3`
y = −2
2x − y + k = 0 (x = 3, y = −2)
2(3) − (−2) + k = 0
6 + 2 + k = 0
k = −8
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