Answer:
the coordinates of the point that partitions the directed line segment from (-6,-2) to (9,-7) into a ratio of 3 to 2 are (0, -4).
Explanation:
To find the coordinates of the point that partitions the directed line segment from (-6,-2) to (9,-7) into a ratio of 3 to 2, we can use the following formula:
P = ( (2bx + 3ax)/(2+3) , (2by + 3ay)/(2+3) )
where P is the point we are looking for, (ax, ay) and (bx, by) are the coordinates of the two endpoints of the line segment, and the numbers 2 and 3 represent the ratio in which the line segment is to be divided.
Substituting the given values, we get:
P = ( (29 + 3(-6))/(2+3) , (2*(-7) + 3*(-2))/(2+3) )
= ( (18 - 18)/5 , (-14 - 6)/5 )
= ( 0, -4 )
Therefore, the coordinates of the point that partitions the directed line segment from (-6,-2) to (9,-7) into a ratio of 3 to 2 are (0, -4).