Answer :
The coordinates of point $p$ along the directed line segment $ab$ is at the point (2.8, -1).
Step 1
To find the coordinates of P so that AP to PB is the given ratio, first look for the slope in rise over run form.
Then, determine the ratio by thinking of it as dividing into segments.
After, add the ratio (in fraction or in decimal) of the run to the x-coordinate and add the ratio (in fraction or in decimal) of the rise to the y-coordinate of the first point in the line segment.
Step 2
First, let us find the slope of the line through rise over run and do not simplify the slope:
[tex]m = \frac{rise}{run}\\ \\m = \frac{1-(-4)}{6-(-2)} \\\\= \frac{5}{8}[/tex]
Since the ratio is 3:2, we want to partition the entire segment into 5 parts with P located at 3\5 of the segment from point A. Therefore, we add 0.6 of the run to the x−coordinate and of the rise to the
y−coordinate:
rise=5⋅0.6=3 y=−4+3=−1
run=8⋅0.6=4.8 x=−2+4.8=2.8
Therefore, the point is at (2.8,−1).
Hence the answer is the coordinates of point $p$ along the directed line segment $ab$ is at the point (2.8, -1).
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