Question 981640: Point A is located at (0, 4), and point B is located at (−2, −3). Find the point that is 1 over 4 the distance from point A to point B.
A. (−1, 0.75)
B. (−0.75, 2)
C. (−0.5, 2.25)
D. (−0.25, 3)
i think its C??
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! (1) Find equation of the line containing the given points. Put into slope-intercept form.
(2) Distance formula, to find distance AB.
(3) Distance formula again, using the unknown point (x,y) to be  of distance from (0,4). y will be in terms of x, according to the equation of the line found. Solve for x, and use it to find corresponding y.
That is the plan and description of the process, which YOU can do.
SOLUTION PROCESS DETAILS
(1)
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pick either point
----but y intercept already given as one of the points.
(2)
(3)
The general unknown point on the line is (x,y) or (x,(7/2)x+4).
Point A is (0,4).
You want (x,y) so that
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The steps to simplify that equation
Notice that x is already isolated in one term and no need to square both sides as
part of this simplification!....
because sqrt(x^2) might be positive or negative x;
 --------------one of these will make sense and one will not make sense.
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What then is the y coordinate?
 ,......
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