Question 1197212: The segment joining P1(2,-4) and P2(9,3) is divided into two segments. One of which is three-forths as long as the other. Find the point of division nearer to P2. Plot the points and draw the line segment.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Since the shorter segment is 3/4 as long as the longer, let the lengths of the two segments by 3x and 4x.
Then, working with the x- and y-coordinates separately, divide the difference between the coordinates of the two points into 7 equal parts. Since the point of division is to be closer to (9,3), the difference between (9,3) and the coordinates of the point of division should be 3 of those 7 equal parts.
The difference between the x-coordinates is 7; so that difference will be divided into parts of 3 and 4. The difference in the y-coordinates is also 7, so that will also be divided into parts of 3 and 4.
The x coordinate of the point of division will be a distance of 3 from 9 towards 2, making it 6; the y coordinate will be a distance of 3 from 3 towards -4, making it 0.
ANSWER: (6,0)
You can draw the figure....
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