CC Geometry H Aim #3: How do we rotate points 90 degrees on the coordinate plane? Do Now:

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CC Geometry H Aim #3: How do we rotate points 90 degrees on the coordinate plane? Do Now: 1. a. Write the equation of the line that has a slope of m = and passes through the point (0, 3).

3 CC Geometry H Aim #3: How do we rotate points 90 degrees on the coordinate plane? Do Now: 1. a. Write the equation of the line that has a slope of m = and passes through the point (0, 3). Graph this equation on the grid provided. b. Graph the equation of the line y - 2 = 4(x - 4) on the same grid. c. Compare the slopes of the two lines. y - 2 = 4(x - 4) 2. a. Graph the lines y = x + 2 and y = x - 1 on the grid provided. y = x + 2 b. Compare the slopes of the two lines. 3. a. Graph the lines y = x + 2 and y = -x + 2 on the grid provided. b. Compare the slopes of the two lines. y = x + 2 In each graph above, the two lines are to each other. lines form 90 o angles. How are the slopes related? What is the product of the slopes?

4 1) Give the slope of a line that is perpendicular to a line with a slope of: a) 6 b) -1/3 c).25 d) -0.3 e) 7/5 f) -2 Example: 1) How do we rotate the point A(-2,-5) about the origin 90 o and -90 o? a. Plot (0,0) and (-2,-5). Draw the segment. b. What is the slope of the segment? c. Express the slope of the rotated segment two ways:, d. Plot A', the result of R (0,0), 90 o e. Plot A", the result of R (0,0), -90 o On your own: 2) Rotate the point B(2, 3) about the origin 90 o and -90 o? a. Plot (0,0) and (2, 3). Draw the segment. b. What is the slope of the segment? c. Express the slope of the rotated segment two ways:, d. Plot B', the result of R (0,0), 90 o e. Plot B", the result of R (0,0), -90 o 90 o Rotations about the Origin (0,0) Plot A', the image of A(x,y) after a 90 o counterclockwise rotation about the origin. The slope of OA = CCW A(x,y) The slope of OA' =. What is the relationship between the two slopes? What is the product of the slopes? O R O,90 (x,y) = (, ) Plot A", the image of A(x,y) after a 90 o clockwise rotation about the origin. The slope of OA =. O A(x,y) 90 0 CW or 90 0 The slope of OA" =. R O,-90 (x,y) = (, )

5 Example: The line segment connecting A(3,7) to B(10,1) is rotated CCW and CW 90 o about A. a) Plot the points and draw the segment. b)what is the slope of the hypotenuse (segment)? c) Express the slope of the rotated segment two ways d) Plot B', the result of a 90 o CCW rotation of B about A, and B", the result of a 90 o CW rotation of B about A. State the coordinates of B' and B". 1) If the line segment connecting the point P (5,2) to R (3,6) is rotated 90 o CCW about point R: a) What is the slope of the original segment, PR? b) What is the slope of the rotated segment? c) Where will point P land? 2) ST has endpoints S(-2,-1) and T (1,4). a) What is the slope of the original segment? b) What is the slope of the rotated segment? c) Where does point T land if the segment is rotated 90 o CCW about S? b) Where does point T land if the segment is rotated 90 o CW about S?

6 3) State the coordinates of the image of X(-5, -2) after a rotation 90 o CCW and CW about Y(1, 3). 4) What are the new coordinates of the point (5,1) if it is rotated about the origin: a) 90 o b) -90 o c) 270 o d) 180 o e) -360 o 5) A line through the origin has a slope of 1 / 3. Carl thinks the slope of a perpendicular line at the origin will be 3. Do you agree? Explain why or why not. Let's Sum It Up! Slopes of perpendicular lines are opposite reciprocals of each other. The product of the slopes of perpendicular lines is -1.

7 Name CC Geometry H Date HW #3 1) If a line has the given slope, write the slope of a perpendicular line. a) -4 b) 2.9 c) 0.6 d) 1 e) 0 2) a. Write an equation of the line through the origin with slope ½. b. Write the equation of a line perpendicular to this line that also passes through the origin. 3) What are the coordinates of the point (-3,-4) after a rotation about the origin: a. 90 o CCW b. 90 o CW 4) Find the new coordinates of point (1,4) if it rotates about the origin: a. 90 o CCW b. 90 o CW c. 180 o d. 270 o CCW 5) Line segment ST connects points S(7,1) and T (2,4). a) Where does point T land if the segment is rotated 90 o counterclockwise about S? b) Where does point T land if the segment is rotated 90 o clockwise about S? c) Where does point S land if the segment is rotated 90 o counterclockwise about T? d) Where does point S land if the segment is rotated 90 o clockwise about T?

8 6) Write an equation of the line perpendicular to the line with equation y = -4x + 1 and which passes through (0,-2). 7) Line segment VW connects points V (1,0) and W (5,-3). a) Where does point W land if the segment is rotated 90 o CCW about V? b) Where does point W land if the segment is rotated 90 o CW about V? c) Where does point V land if the segment is rotated 90 o CCW about W? d) Where does point V land if the segment is rotated 90 o CW about W? Review: 1. Find the number of people who live in NYC if there are approximately 17,620 people per square mile in NYC and NYC is 468 square miles. Note: population density = number of people area of land 2. If BC = 10 and AB = 16, find to the nearest tenth, the measure of the largest acute angle in the triangle.

A A B B C C D D. NC Math 2: Transformations Investigation

A A B B C C D D. NC Math 2: Transformations Investigation NC Math 2: Transformations Investigation Name # For this investigation, you will work with a partner. You and your partner should take turns practicing the rotations with the stencil. You and your partner