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Question
In what ratio does the point Q(1, 6) divide the line segment joining the points P(2, 7) and R(−2, 3)
Options
1 : 2
2 : 1
1 : 3
3 : 1
Solution
1 : 3
Explanation;
Hint:
A line divides internally in the ratio m : n the point P
= `(("m"x_2 + "n"x_1)/("m" + "n"), ("m"y_2 + "n"y_1)/("m" + "n"))`
(1, 6) = `((-2"m" + 2"n")/("m" + "n"), (3"m" + 7"n")/("m" + "n"))`
= `(-2"m" + 2"n")/("m" + "n")` = 1
−2m + 2n = m + nx
−3m = n – 2n
3m = n
`"m"/"n" = 1/3`
∴ m : n = 1 : 3
and
`(3"m" + 7"n")/("m" + "n")` = 6
3m + 7n = 6m + 6n
6m – 3n = 7n – 6n
3m = n
`"m"/"n" = 1/3`
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