Answer: A partition of a line segment is a point that divides the segment into a certain ratio of segments. In this case, point P partitions the segment AB in the ratio 3 to 1.
To find the coordinates of point P, we can use the following method:
Let the point P be (x,y)
The ratio of the segments AP:BP is 3:1, so we can use the proportion: (AP)/(BP) = 3/(1+3) = 3/4
We can use the coordinates of points A and B to find the coordinates of point P. The x-coordinate of P is (3/4) times the difference in x-coordinates of A and B, plus the x-coordinate of A. And the y-coordinate of P is (3/4) times the difference in y-coordinates of A and B, plus the y-coordinate of A.
So, using the coordinates of A and B:
x = (3/4)(-5 - 7) + 7 = -4
y = (3/4)(4 - (-4)) -4 = 3
Therefore, the coordinates of point P are (-4,3)
Explanation: