SOLUTION: Find the point that is one-eighth the distance from the point P(8,8) to the point Q(-7,-7) along the segment PQ

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Question 181784: Find the point that is one-eighth the distance from the point P(8,8) to the point Q(-7,-7) along the segment PQ
Answer by solver91311(24713) (Show Source):
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Find the point that is one-eighth the distance from the point P(8,8) to the point Q(-7,-7) along the segment PQ.

The first thing to notice is that the x-coordinate of P equals the y-coordinate of P and x-coordinate of Q equals the y-coordinate of Q. That means the segment PQ lies on the line described by:

The distance formula:

gives us that the distance from P to Q is:

One eighth of that distance is then

The distance from P(8,8) to the desired point, call it R(x, y) is then given by;

But remember that this point must lie on the line

So we can re-write the distance equation:

But this distance needs to be one-eighth of the distance from P to Q which we have already established to be , meaning that we can now write:

Multiplying both sides by yields:

Collect, apply LCD of 8, and multiply by -1:

And since

And finally, the desired point is

John