To find the coordinates of the point that partitions the directed line segment from ( − 5 , 4 ) to ( 1 , 8 ) into a ratio of 3 to 1, we can use the following formula:
(x,y) = (1- t) * (x1, y1) + t * (x2, y2)
Where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the directed line segment, t is a value between 0 and 1 that represents the ratio of the partition, and (x, y) are the coordinates of the point that partitions the segment.
In this case, we want the ratio of the partition to be 3 to 1, so t = 3 / (3 + 1) = 3/4
So we can substitute the values into the formula:
(x,y) = (1- 3/4) * (-5, 4) + (3/4) * (1, 8)
(x,y) = (-5/4, 4/4) + (3/4, 6/4)
(x,y) = (-5/4+3/4, 4/4+6/4)
(x,y) = (-2/4, 10/4)
(x,y) = (-0.5, 2.5)
So the point that partitions the directed line segment from ( − 5 , 4 ) to ( 1 , 8 ) into a ratio of 3 to 1 has coordinates (-0.5, 2.5)