Question

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Find the coordinates of the point P that divides the directed line segment from A to B in the given ratio.

A(-6, 9), B(2, 1); Ratio 5 to 3

Answer 1

The coordinates of the point P = (x, y) = (-1, 4)

Explanation:

Let the coordinates of P be (x, y)

• (x₁, y₁) = (-6, 9)

• (x₂, y₂) = (2, 1)

• ratio = m:n = 5:3

Using the section formula

x = [(mx₂ + nx₁)] / [(m+n)]

= [5(2)+3(-6)] / [5+3]

= [10-18] / [8]

= -8/8

= -1

y = [(my₂ + ny₁)] / [(m+n)]

= [5(1)+3(9)] / [5+3]

= [5+27] / [8]

= 32/8

= 4

Therefore, the coordinates of the point P = (x, y) = (-1, 4)