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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`
Solution
∴ 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
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