Final answer:
To find the coordinates of point P that lies along the directed line segment from M(-3,-3) to N(4,2) and partitions the segment in the ratio of 3 to 2, we can use the section formula. The coordinates of point P are (1, -1).
Step-by-step explanation:
To find the coordinates of point P that lies along the directed line segment from M(-3,-3) to N(4,2) and partitions the segment in the ratio of 3 to 2, we can use the concept of section formula. The section formula states that if the coordinates of two points A(x1,y1) and B(x2,y2) are given, and a point P divides the segment AB in the ratio m:n, then the coordinates of point P can be found using the following formulas:
x = (mx2 + nx1) / (m+n)
y = (my2 + ny1) / (m+n)
Plugging in the values from the question, we can find the coordinates of point P:
x = (3*4 + 2*(-3)) / (3+2) = 1
y = (3*2 + 2*(-3)) / (3+2) = -1
Therefore, the coordinates of point P are (1, -1).