Points, Lines, and Planes

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Presentation transcript:

Points, Lines, and Planes 1.1 Points, Lines, and Planes Splash Screen

1. Solve 2(x – 7) = 5x + 4. A. –6 B. C. 2 D. 6 5-Minute Check 2

2. Which is a solution of 3x + 4y = 14? B. (–2, 5) C. (1, 3) D. (2, 3) 5-Minute Check 3

3. Factor 9x2 – 25y2. A. (3x – 5y)2 B. (3x + 5y)2 C. (3x + 5y)(3x – 5y) D. (9x + 5y)(x – 5y) 5-Minute Check 4

4. Graph y = 3x + 2. A. B. C. D. 5-Minute Check 5

undefined term defined term space point line plane collinear coplanar intersection Vocabulary

\ \ \ \ \ \ \ Concept

A. Use the figure to name a line containing point K. Name Lines and Planes A. Use the figure to name a line containing point K. Answer: Example 1

B. Use the figure to name a plane containing point L. Name Lines and Planes B. Use the figure to name a plane containing point L. Answer: Example 1

A. Use the figure to name a line containing the point X. A. line X B. line c C. line Z D. Example 1a

B. Use the figure to name a plane containing point Z. A. plane XY B. plane c C. plane XQY D. plane P Example 1b

A. Name the geometric shape modeled by a 10  12 patio. Model Points, Lines, and Planes A. Name the geometric shape modeled by a 10  12 patio. Answer: Example 2

B. Name the geometric shape modeled by a button on a table. Model Points, Lines, and Planes B. Name the geometric shape modeled by a button on a table. Answer: Example 2

A. Name the geometric shape modeled by a colored dot on a map used to mark the location of a city. A. point B. line segment C. plane D. none of the above Example 2a

B. Name the geometric shape modeled by the ceiling of your classroom. A. point B. line segment C. plane D. none of the above Example 2b

Draw a surface to represent plane R and label it. Draw Geometric Figures Draw a surface to represent plane R and label it. Example 3

Draw Geometric Figures Answer: Example 3

Draw Geometric Figures Answer: There are an infinite number of points that are collinear with Q and R. In the graph, one such point is T(1, 0). Example 3

A. Choose the best diagram for the given relationship A. Choose the best diagram for the given relationship. Plane D contains line a, line m, and line t, with all three lines intersecting at point Z. Also, point F is on plane D and is not collinear with any of the three given lines. A. B. C. D. Example 3a

A. How many planes appear in this figure? Interpret Drawings A. How many planes appear in this figure? B. Name three points that are collinear. C. Are points A, B, C, and D coplanar? Explain. Example 4

A. How many planes appear in this figure? A. one B. two C. three D. four Example 4a

B. Name three points that are collinear. A. B, O, and X B. X, O, and N C. R, O, and B D. A, X, and Z Example 4b

C. Are points X, O, and R coplanar? A. yes B. no C. cannot be determined Example 4c

A. point X B. point N C. point R D. point A Example 4d