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Question
Point C divides the line segment whose points are A(4, –6) and B(5, 9) in the ratio 2:1. Find the coordinates of C.
Solution
Given points are A(4, –6) and B(5, 9) and the ratio is 2:1.
Let the coordinates of C be (x, y).
Then, by the section formula,
x = `(mx_2 + nx_1)/(m + n)`
= `(2 xx 5 + 1 xx 4)/(2 + 1)`
= `(10 + 4)/3`
= `14/3`
y = `(my_2 + ny_1)/(m + n)`
= `(2 xx 9 + 1 xx (-6))/(2 + 1)`
= `(18 - 6)/3`
= `12/3`
= 4
As a result, the coordinates of point C are `(14/3, 4)`.
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