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What are the coordinates of point P on the directed line segment from A to B such that P is One-fourth the length of the line segment from A to B?

User Bob
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2 Answers

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Answer:

the coordinate of P is (-11/4, -1/2)

x= -11/4

y= -1/2

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Explanation:

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User Darrien
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5 votes

Answer:

The answer is explained below

Explanation:

The location of point A = (-5, -1) and point B = (4, 1).

To find the coordinate of the point that divides a line segment PQ with point P at
(x_1,y_1) and point Q at
(x_2,y_2) in the proportion a:b, we use the formula for the x and y coordinates:


x-coordinate:\\(a)/(a+b)(x_2-x_1)+x_1 \\\\While \ for\ y-coordinate:\\(a)/(a+b)(y_2-y_1)+y_1

P is One-fourth the length of the line segment from A to B, Therefore AB is divided in the ratio 1:4. The location of point A = (-5, -1) and point B = (4, 1).Therefore:


x-coordinate:\\(1)/(1+3)(4-(-5))+(-5)=(1)/(4)(9)-5=-(11)/(4) \\\\While \ for\ y-coordinate:\\(1)/(1+3)(1-(-1))+(-1)=(1)/(4)(2)-1=(-1)/(2)

Therefore the coordinate of P is (-11/4, -1/2)

User Merita
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