What is the value of k used to find coordinates of a point that partitions a segment into a ratio of 5: 3? (explain with work). someone ! my teacher can't teach and i have a bunch of questions i have to answer.

The value of k is 5/8.

Problem 22

Explanation:

Segments XY and YZ add up to segment XZ

XY + YZ = XZ

(x+6) + (3x+1) = 5x

4x+7 = 5x

7 = 5x-4x

7 = x

x = 7

Problem 23

Explanation:

We'll use the result in the previous problem to find that,

XY = x+6

XY = 7+6

XY = 13

Problem 24

Explanation:

Similar to problem 23, we'll use the value of x = 7 to find that,

YZ = 3x+1

YZ = 3*7+1

YZ = 21+1

YZ = 22

Problem 25

Explanation:

We have two options. We could add the results of the last two problems

XZ = XY + YZ = 13+22 = 35

Or we could compute XZ directly like so

XZ = 5x = 5*7 = 35

Either way, we get the same result. The fact we get the same value both times helps confirm we have the correct x value and the correct lengths of XY and YZ.