Answer:
Option C is the correct answer.
Step-by-step explanation:
Given:
The coordinates of the point A and B are (-5,-1) and (4,1)
The 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.
Thus, we have;
m=1 and m+n=4
We need to determine the coordinates of the point P(x,y)
x - coordinates of the point P:
The x - coordinates of the point P can be determined using the formula
x=(m/m+n)(x₂ - x₁)+ x₁
Substituting the values, we get;
x= 1/4(4+5)-5
x = 9/4-5
x = -11/4
Thus, the x - coordinate of the point P is -11/4
y - coordinate of the point P:
The y - coordinate of the point P can be determined using the formula,
y=(m/m+n)(y₂ - y₁)+ y₁
Substituting the values, we get;
y= 1/4(1+1)-1
y = 2/4-1
y= -2/4
y= -1/2
Thus, the y - coordinate of the point P is -1/2
Therefore, the coordinates of the point P is (-11/4, -1/2)
Hence, Option C is the correct answer.
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