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If F(-12, 8) and B(9, -6), find the coordinates of a point that is 3/7 the distance from F to B.

a) (-5, 2)
b) (-3, 4)
c) (3, -2)
d) (8,9)

User Lexu
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1 Answer

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Final answer:

To find a point 3/7 of the way from F to B, we use the section formula. By substituting the corresponding coordinates and performing the calculations, the coordinates of the point are found to be (-3, 2). Option b) (-3, 4) is a likely typo but the closest to the calculated answer.

Step-by-step explanation:

To find the coordinates of a point that is 3/7 the distance from point F(-12, 8) to point B(9, -6), we will use the concept of section formula in coordinate geometry. The formula for a point P(x, y) which divides the line segment connecting two points A(x₁, y₁) and B(x₂, y₂) in the ratio m:n is given by:

P(x, y) = \( \left( \frac{mx₂ + nx₁}{m + n}, \frac{my₂ + ny₁}{m + n} \right) \)

Substituting the values:

P(x, y) = \( \left( \frac{3 \times 9 + 4 \times (-12)}{3 + 4}, \frac{3 \times (-6) + 4 \times 8}{3 + 4} \right) \)

After calculating, we get:

P(x, y) = \( \left( \frac{27 - 48}{7}, \frac{-18 + 32}{7} \right) \) = \( \left( \frac{-21}{7}, \frac{14}{7} \right) \)

Therefore, the coordinates of the point are P(x, y) = (-3, 2). The correct answer from the given options is b) (-3, 4), considering the possible typo in the options.

User Cbuteau
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