Geometry Name: Geometry Unit 2: Linear Topics Covered: Midpoint formula Distance formula Slope Slope- Intercept Form Point- Slope Form Standard Form Assignment # Section Page and Problems Date Assigned 6 Midpt Pg. 37 #1-5, 8 9.5 Pg. 504 #1, 2, 5 Review Pg. 140 #4, 5, 6, 7, 19, 25 7 9.5 Pg. 504 #4, 7, 8, 10 lines Pg. 169 #1, 2, 3, 4 Slope Pg. 136 #1, 2, 3, 4 Eq.s Pg. 214 #3, 4, 5, 6, 7, 8, 10 8 Slope- Intercept Form WKST 9 Point- Slope Form WKST 10 Standard Form WKST 11 Unit 2 Linear Study Guide Due Date 1
Geometry Review: What are the coordinates of the following points? A = ( ) B = ( ) C = ( ) D = ( ) E = ( ) Graph the following points. F(- 3, 2) G(4, 1) H(0, 3) I(- 1, 0) What is the midpoint of a segment? Midpoint and Distance Formula Look at the graph to the right, what are the coordinates of the midpoint the segment? of 2
Midpoint Formula Example: Find the midpoint of the segment with endpoints (- 3, 7) and (- 5, 3). Example: Find the midpoint of AB, where A(8, - 2) and B(1, - 8). Your Turn! 1) Find the midpoint of the segment with endpoints (4, 0) and (2, - 10). 2) What is the midpoint of segment CD, where C(11, - 3) and D(- 5, 0)? What if you have one endpoint and the midpoint? Example: If the midpoint of EF is (4, - 2) and E(6, 0), what are the coordinates of F? Graph: Algebraically: 3
Example: The midpoint of GH is (3, 4) and the coordinates of H are (- 1, 0), what are the coordinates of G? Graph: Algebraically: Distance Formula Example: Find the distance between (3, 2) and (- 3, 0). Round to the nearest hundredth (2 decimal places). Example: Find the length of IJ, if I(9, 1) and J(4, - 3). Round to the nearest hundredth. Your Turn! Find the distance between the two points. 1) (3, - 2) and (2, 4) 2) (1, 4) and (6, 3) 4
Geometry Review: Simplify the following using order of operations 1)!!!!!!!! 2) 4 2 6 + 1 9! 3) 3 4! + 5 + 1! Slope: Slope is: Slope Formula m = y! y! x! x! Find the slope between the two points a) (2, - 3) and (7, 4) 5 b) (4, 6) and (4, 0)
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Example 1: Find the slope of each of the following graphs Slope Practice A) B) C) Example 2: Find the slope between the two given points. Find the slope of a parallel line and a perpendicular line. A) (3, - 2) and (1, - 7) B) (5, 6) and (3, 6) Slope: Parallel Slope: Perpendicular Slope: Slope: Parallel Slope: Perpendicular Slope: C) (4, - 5) (- 3, - 7) D) (2, 8) and (2, 0) Slope: Parallel Slope: Perpendicular Slope: Slope: Parallel Slope: Perpendicular Slope: 8
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Geometry Review: Graph the following a) a line with slope of 2 b) a line with slope of 0 c) a line with undefined slope d) a line passing through (4, 3) and (- 2, 1) Challenge: a line with endpoint (1, 1) and midpoint (- 2, 0) Graphing Slope Intercept Form 1) Start at 2) Move Graph in BLUE y = 1 4 x + 2 Slope Intercept Form y = mx + b Graph in RED y = 3x 4 How to Write the Equation of a Line in SLOPE INTERCEPT Form 1. Determine 2. Find Ex. Write the equation of the line in slope- intercept form Ex. Write the equation of a line passing through (0, 8) and (- 3, 4) 11
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Slope- Intercept Practice Special Graphs Horizontal Line Vertical Line Example: Graph the following a) y =! x 5 b) y = 3x + 1 c) y = 2x! Example: Write the equation of a line passing through (8, 3) and (0, - 5). Example: Write the equation of a line passing through (3, - 7) and (0, 1). 13
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Geometry Review: For the following identify the slope and y- intercept (if exists). a) y = 6x + 1 b) y =! x 9! c) y = 5x Slope - Slope- Slope- y- intercept - y- intercept- y- intercept d) y = 8 e) x = 3 Slope- Slope- y- intercept- y- intercept- y y! = m(x x! ) Point Slope Form Graphing Point- Slope Form 1. Determine 2. Move Graph y 6 =! (x + 2) in blue! Point (, ) Slope = Graph y + 1 = 2(x 3) in red Point (, ) Slope = How to Write the Equation of a Line in POINT- SLOPE Form 1. Determine the 2. Plug in and into y y! = m(x x! ) Ex. Write the equation of a line passing through (5, 4) and (- 3, - 2) in POINT- SLOPE form. Ex. Write the equation of a line PARALLEL to y = 4x + 2 and passing through (10, 1) in POINT- SLOPE form. Ex. Write the equation of a line PERPENDICULAR to y =! x + 2 and passing through (8, 0) in POINT- SLOPE! form. 15
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Point- Slope Practice Example: Graph the following a) y 2 =!! x 2 b) y + 1 = 4(x + 3) Example: Write the equation of a line passing through (- 5, - 6) and (7, 1) in POINT- SLOPE form. Example: Write the equation of a line passing through (6, 1) and PARALLEL to y = 3x in SLOPE- INTERCEPT form. Example: Write the equation of a line PERPENDICULAR to y = 2x 6 and passing through (- 3, - 7). 17
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Geometry Review: For each of the following determine the slope of the line a) y = 6x + 3 b) line passing through (0, 3) and (- 2, - 7) c) y + 2 =! (x 3)! Standard Form Ax + By = C Graphing Standard Form 1) Find and graph the x- intercept (cover the ) 2) Find and graph the y- intercept (cover the ) 3) Connect intercepts Graph 4x + 6y = 12 Graph 2x 3y = 6 Standard Form 19