Unit 1 Test – Study Guide Algebra Nation Section 1 Topics 1 – 8

Click Here for the Khan Academy Alignment & Video Suggestions

Textbook Alignment (HOLT GREEN: 1.1, 1.2, 1.6, 3.4 – 3.6 LARSON BLUE: 1.1, 1.2 1.3, 3.3 – 3.6)

Note: For each vocabulary word, you should know the definition, the visual, and the symbol. Many of these words will

indicate what type of problem is being asked and which concept/formula to apply.

Vocabulary: (Building Blocks of Geometry: point, line, plane), ray, segment, parallel, perpendicular, collinear, coplanar,

opposite rays, midpoint, halfway, segment addition postulate, equidistant, congruent, length, distance, partition, ratio, k,

slope-intercept form, perpendicular bisector.

All formulas must be MEMORIZED. Write each formula down 20x to commit to memory.

Segment Addition Postulate

DE + EF = DF

5x – 2 + 3 = 3(x + 3)

Distance Formula Partitioning a Line Segment

Slope

Slope Intercept Form (Equation of a Line)

Parallel Lines: same slope (ex. ¼ and ¼ ) Perpendicular Lines: negative reciprocals (ex. ½ and –2)

Topics 1.1 and 1.2

Diagram 1 Diagram 2

1. Describe what is happening in each of the diagrams above using the words: (intersecting, parallel, perpendicular,

line segment, plane, collinear, coplanar).

2. Diagram 2: Name line FA in 3 other ways.

3. Diagram 2: Name 2 pairs of opposite rays.

4. Diagram 1: Name the intersection of line m and Plane T.

5. Diagram 1: Does line m lie in Plane T?

6. Diagram 2: Does line FA lay in plane D and/or in Plane N? Explain.

7. Draw a diagram of ray 𝐷𝐹⃗⃗⃗⃗ ⃗ that is perpendicular to plane Q and intersecting the plane at point O. Draw 2 lines

that lie on plane Q that intersect at point O. Call the lines 𝐴𝐾⃡⃗⃗⃗ ⃗ and line s. Draw a parallel plane called plane P and

draw a pair of opposite rays that lie on the plane.

8. Draw a diagram of the 3 building blocks of geometry and label them using proper naming syntax

Topics 1.3 & 1.4

Segment Addition Postulate:

1. Points A, B and C are collinear on AC. If AB is 3

times larger than BC and AC = 20, what is the length

of AB and BC?

2. Points R, S and U are collinear on RU. If RU is 4

times larger than SU and RS is 12, what is the length

of RU and SU?

Midpoint

1. Donald Duck says the midpoint of (4, 2) and (10, –3) is

(7, 0). Is he right? Justify your answer.

2. What is the midpoint of (3, 1) and (–5, 12)?

Distance

3. What is the length of ST, S(4, -1) and T(6,0)?

4. What is the distance between the points (-2,-8) and

(-3, -12)?

5. What is the perimeter of ABC if A (3, 0), B (5, -6) and

C(-1, 10)?

Topics 1.5 and 1.6

Partitioning a Line Segment (draw a visual to help you and pay close attention to the details provided)

Drill (finding k)

1. Point P partitions line segment DF into the ratio 4:5, what is k?

2. Points A,R,K are collinear on segment AK. The ratio of AR:AK is 2

7, what is k?

4. Point K is located on AF. The ratio of AK:KF is 7:8. What is k?

5. What is the difference between the ratio AP:PB and the ratio AP:AB?

6. Point T is on line segment AE. Point T will be placed on segment AE so that it partitions it into a ratio of 2:3.

There are 2 locations that point T can assume. Draw a sketch of each location that point T can assume and

write down the corresponding k value for each example.

Finding a Point that Partitions OR the Endpoint

1. Draw a sketch

2. Assign (x1,y1) and (x2,y2) as the endpoints, (x,y) is the partitioning point

3. Substitute the values into the partitioning formula: remember the x and y are the partitioning point

values

x = x1 + k(x2 – x1) y = y1 + k(y2 – y1) *if an endpoint is missing, make it (x2,y2)

4. Solve for the missing x and y values

7. Point D is collinear with points A and K on 𝐴𝐾. A is at (7, 2) and K is at (2, -10). Point D partitions AK in a

ratio of 5:1. Point D can assume 2 different locations. Find each location of D.

8. Points A, B and C are collinear on 𝐴𝐶, and AB:BC = 3

4. A is located at (x,y), B is located at (4,1) and C is

located at (12,5). What are the values of x and y?

9. Points G, K and J are collinear on 𝐺𝐽, and GK:GJ = 3

5. G is located at (-4,5), K is located at (x,y), and J is

located (6,0). What are the values of x and y?

10. Points A, P and B are collinear on 𝐴𝐵, and PB:AB = 2/7. A is located at the origin, P is located at (10,-5)

and B is located at (x,y).

11. Point A partitions 𝐷𝐹 in a ratio of 2:5. D is at (4,1) and F is at (10, -12), what is the coordinate of A?

Topics 1.7 and 1.8

Finding the Equation of a Line Parallel or Perpendicular

Skill Building Drills:

A) Rewrite each equation in slope intercept form (y = mx + b) and find the m and b values.

B) Write the equation of the line that passes through the given points and has the given slope.

1. Passes through (2,3) and slope is 5.

2. Passes through (6, –5) and slope is –1/3

C) Identify if the lines in example 1 and example 2 are parallel, perpendicular or neither?

D) Which lines are parallel, perpendicular or neither? a graph may help

A) x = 4 B) y = –2 C) x = 2 D) y = 4x E) 8y = –2x + 1 F) y = 1

1. Write the equation of a line parallel and a line perpendicular to the line 5y = –2x – 20 and passes through the

point (–10, 8).

2. Write the equation of a line that passes through (4,0) and is parallel and perpendicular to 2x + y = 1.

ST

EP

S

Additional Resources:

Slope Intercept Form:

http://psn.virtualnerd.com/viewtutorial/Alg1_10_2_8

Parallel Lines:

http://psn.virtualnerd.com/viewtutorial/Alg1_10_2_11

Equation of Parallel Line through a Point:

http://www.virtualnerd.com/algebra-1/linear-equation-

analysis/parallel-perpendicular-lines/parallel-lines/slope-

intercept-from-point-and-parallel-line

Equation of Perpendicular Line through a Point:

http://www.virtualnerd.com/algebra-1/linear-equation-analysis/parallel-perpendicular-lines/perpendicular-lines/slope-

intercept-from-point-and-perpendicular-line

Sample Workouts: