In exercises 7 and 8, identify the segment bisector of jk. then find jm.

The segment bisector is either a point, a line segment, a ray or a line that bisects another line

The solution to the questions are;

7. Part A; The midpoint is the point M

Part B; JM = 40

8. Part A; The midpoint is the line l

Part B; JM = 9

The basis for the above values is presented here as follows:

7. Part A

From the given diagram of the line with point M, we have;

JM = 7·x + 5

KM = 8·x

From the same length symbol, we have;

Segment JM = Segment KM

Therefore, the segment bisector is the point marked M

Given that JM = KM, by substitution property, we have;

7·x + 5 = 8·x

Therefore;

5 = 8·x - 7·x = x

5 = x

∴ x = 5

The length of JM = 7·x + 5

∴ JM = 7 × 5 + 5 = 40

JM = 40

8. Part A

The given diagram is a line JK being bisected by the line l

JM = 3·x + 15

KM =  8·x + 25

From the same length symbol, we have;

Segment JM = Segment KM

Therefore, the midpoint = The point M

The line l that marks the midpoint M on the line segment JK is the segment bisector, and we have;

The segment bisector = The line l

Part B

Given that JM = KM, by substitution property, we get;

3·x + 15 = 8·x + 25

Therefore;

3·x - 8·x = 25 - 15

-5·x = 10

x = 10/(-5) = -2

x = -2

JM =  3·x + 15

Therefore;

JM =  3 × (-2) + 15 = 9

The length of segment JM = 9

In conclusion, a segment bisector is the point or line that bisects another line

Learn more about segment bisectors here;

link

#7) M is the Midpoint of JK. Since there is no segment through M, then there is no segment bisector.

JM = 7x + 5, MK = 8x (Given)

JM ≡ MK (definition of midpoint)

JM = MK (definition of congruency)

7x + 5 = 8x (substitution)

5 = x (subtraction property of equality)

JM = 7x + 5 → JM = 7(5) + 5 → JM = 35 + 5 → JM = 40

#8) M is the Midpoint of JK. the line passing through M is line l, so line l is the segment bisector.

JM = 3x + 15, MK = 8x + 25 (Given)

JM ≡ MK (definition of midpoint)

JM = MK (definition of congruency)

3x + 15 = 8x + 25 (substitution)

15 = 5x + 25 (subtraction property of equality - subtracted 3x)

-10 = 5x (subtraction property of equality - subtracted 25)

-2 = x (division property of equality)

JM = 3x + 15 → JM = 3(-2) + 15 → JM = -6 + 15 → JM = 9

5

step-by-step explanation: