Question

activity 4 practice
write your answers on notebook paper.
show your work.
lesson 4 - 1

1. if q is between a and m and mq = 7.3 and am = 8.5, then qa =

a. 5.8
b. 1.2
c. 7.3
d. 14.6

1. given: k is between h and j, hk = 2x - 5, kj = 3x + 4, and hj = 24. what is the value of x?

a. 9
b. 5
c. 19
d. 3

1. if k is the midpoint of (overline{hj}), hk = x + 6, and hj = 4x - 6, then kj =

a. 15
b. 9
c. 4
d. 10

1. state the segment addition postulate in your own words.
2. explain what distance along a line means as an undefined term in geometry.

use the number line for items 6 - 9.

1. what is ab?
2. what is the coordinate of the midpoint of (overline{ab})? explain how you found your answer.
3. point m is the midpoint of (overline{ab}). what is the coordinate of the midpoint of (overline{am})?
4. point c is between points a and b. the distance between points b and c is (\frac{1}{4}) of ab. what is the coordinate of point c?
5. (overline{fg}) lies on a number line. the coordinate of point f is 8. given that fg = 16, what are the two possible coordinates for point g?
6. in the diagram, (overline{st}) is aligned with a centimeter ruler. what is the length of (overline{st}) in centimeters?
7. compare and contrast a postulate and a theorem.
8. what are two conclusions you can draw from this statement? support your answers.

point p is the midpoint of (overline{qr}).

1. if d is the midpoint of (overline{ce}), cd = x + 7, and ce = 5x - 1, determine each missing value.

a. x =
b. cd =
c. ce =
d. de =

1. leo is running in a 5 - kilometer race along a straight path. if he is at the midpoint of the path, how many kilometers does he have left to run?
2. point s is between points r and t. given that (overline{rs}congoverline{st}) and rs = 16, what is rt?

lesson 4 - 2

1. p lies in the interior of (angle rst). (mangle rsp = 40^{circ}) and (mangle tsp = 10^{circ}). (mangle rst=)

a. (100^{circ})
b. (50^{circ})
c. (30^{circ})
d. (10^{circ})

1. (overrightarrow{qs}) bisects (angle pqr). if (mangle pqs = 3x) and (mangle rqs = 2x + 6), then (mangle pqr=)

a. (18^{circ})
b. (36^{circ})
c. (30^{circ})
d. (6^{circ})

1. (angle p) and (angle q) are supplementary. (mangle p = 5x + 3) and (mangle q = x + 3). (x=)

a. 14
b. 0
c. 29
d. 30

Explanation:

Step1: Determine the coordinate of S and T

From the ruler, the coordinate of \( S\) is \(7\) and the coordinate of \(T\) is \(11.5\).

Step2: Calculate the length of \(\overline{ST}\)

Use the formula for the distance between two points on a number line \(d = |x_2 - x_1|\). Here \(x_1 = 7\), \(x_2=11.5\), so \(ST=|11.5 - 7|\).

$$ST=11.5 - 7 = 4.5$$

Answer:

\(4.5\) centimeters