Question

Complete the following activity to find the coordinates of point P which divides seg AB in the ratio 3:1 where A(4, – 3) and B(8, 5).

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`

Answer 1

∴ By section formula,

x = `("m"x_2 + "n"x_1)/bb("m" + "n")`, 

∴ x = `(3 xx 8 + 1 xx 4)/(3 + 1)`, 

= `(bb24 + 4)/4`,

∴ x = `28/4`, 

∴ x = 7

y = `bb("my"_2 + "ny"_1)/("m" + "n")`

y = `(3 xx 5 + 1 xx (-3))/(3 + 1)`

= `(bb15 - 3)/4`

∴ y = `12/4`

y = 3