Line segment xy is a directed line segment beginning at point x(9, 2) and ending at point y(-6, 2). find the point z on the line segment that partitions the line segment into the segments xz and zy at a ratio of 5: 3.

Step-by-step explanation:

Point Z divides XY into a 5:3 ratio, so Z is 5/3 of the way from X to Y.  That ratio is k, found by writing the numerator of the ratio (5) over the sum of the numerator and the denominator (5 + 3 = 8).  Our k value is 5/8.  Now we will find the rise and run values which is the slope of this line segment:

Coordinates are found in this formula:

Filling that in:

which simplifies to

which gives us the final coordinates of Z to be

answer

step-by-step explanation: