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vodka [1.7K]
3 years ago
7

Find the coordinates of point P that lies along the directed line segment AB in a 2:3 ratio given A (-2, 1), B (3, 4).

Mathematics
1 answer:
saul85 [17]3 years ago
5 0

Answer:

P(x,y) = (0,\frac{11}{5})

Step-by-step explanation:

Given

A = (-2,1)

B = (3,4)

m:n = 2:3

Required

Determine the coordinates of P

The coordinate of a point when divided into ratio is:

P(x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})

Where

(x_1,y_1) = (-2,1)

(x_2,y_2) = (3,4)

m:n = 2:3

This gives:

P(x,y) = (\frac{2 * 3 + 3 * -2}{2 + 3},\frac{2 * 4 + 3 * 1}{2 + 3})

P(x,y) = (\frac{6 - 6}{5},\frac{8 + 3}{5})

P(x,y) = (\frac{0}{5},\frac{11}{5})

P(x,y) = (0,\frac{11}{5})

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