Question

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?

Answer 1

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

x= -11/4

y= -1/2

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Explanation:

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Answer 2

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)