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Question
M and N are two points on the X axis and Y axis respectively. P (3, 2) divides the line segment MN in the ratio 2 : 3.
Find:
(i) the coordinates of M and N
(ii) slope of the line MN.
Solution
Let coordinates of M is (a, 0) and M is (0, b).
Point P divides MN in 2 : 3 ratio
`therefore 3 =(3a + 2 xx 0 )/ (3 + 2) " and " 2 =(3xx0+2xx b)/(3+2)`
3a = 15 and 10 = 2b
a = 5 and b = 5
(i) The coordinates of M is (5, 0) and N(0, 5)
(ii) Slope of the line MN `= (0-5)/(5-0) = -1 `
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Activity:
∴ By section formula,
∴ x = `("m"x_2 + "n"x_1)/square`,
∴ x = `(3 xx 8 + 1 xx 4)/(3 + 1)`,
= `(square + 4)/4`,
∴ x = `square`,
∴ y = `square/("m" + "n")`
∴ y = `(3 xx 5 + 1 xx (-3))/(3 + 1)`
= `(square - 3)/4`
∴ y = `square`
