What are the coordinates for the point on Line AB (see figure) that is three times as far from A as from B, and that is in between points A and B?
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The question is essentially asking us to find the coordinates of a point (call point C) such that length AC is 3 times length BC.[email protected] wrote:
What are the coordinates for the point on Line AB (see figure) that is three times as far from A as from B, and that is in between points A and B?
Consider the right triangle with AB as the hypotenuse.
Now divide the two legs into 4 parts.
If we draw a right triangle like so, we'll see that the red triangle is 1/4 the size of the original blue triangle.
IMPORTANT: This means that the distance from A to C is THREE TIMES the distance from C to B. So, point C satisfies the given information.
Now all we need to do is determine the size of the red triangle.
Since the red triangle is 1/4 the size of the blue triangle, its sides have lengths 3/4 and 1 1/2.
So, to the find the coordinates of C, just factor these lengths into the coordinates of point B.
So, the x-coordinate of point C = (-2) - (3/4) = -2 3/4 (aka -2.75)
The y-coordinate of point C = (0) + (1 1/2) = 1 1/2 (aka 1.5)
So the coordinates are [spoiler](-2.75, 1.5)[/spoiler]
Cheers,
Brent
