 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum           A B C Homework Solutions for Session 7 Homework

See solutions for Problems: H1 | H2 | H3 | H4 | H5 | H6    Problem H1

 a. Any three points on the vertical axis will do -- for instance, (0,-3), (0,1), and (0,13). All the points with x-coordinate 0 are on the y-axis. b. Any three points with the y-coordinate of 1 will do -- for instance, (-7,1), (0,1), and (12,1). All the points on this horizontal line have y-coordinate 1. c. Any three points with x-coordinate 3 will do -- for instance, (3,-4), (3,0), and (3,11). A point is on the line v if its x-coordinate is 3. If its x-coordinate is anything other than 3, the point is not on the line. d. The coordinates are (-4,2). e. For instance, (-3,-3), (-2,-2), (0,0), (4,4), (15,15). All of these points are on the line y = x.   Problem H2

 a. There are infinitely many points between the two lines -- for instance, (-32,-1), (-17,1) (0,0), (33,3), (155,3.5), (1000,3.9). b. There are infinitely many points which are not between the two lines -- for instance, (-32,7), (-17,-15), (0,5), (33,7), (155,4.5), (1000,7.9). c. A point is between the two lines if its y-coordinate is greater than -2 and less than 4.   Problem H3  A B C D E F G              (x,y) (x + 3,y - 2) (-x,y) (2x,2y) (x - 1,y + 2) (y,-x) (-y,x)       (2,1) (5,-1) (-2,1) (4,2) (1,3) (1,-2) (-1,2) (-4,0) (-1,-2) (4,0) (-8,0) (-5,2) (0,4) (0,-4) (-5,4) (-2,2) (5,4) (-10,8) (-6,6) (4,5) (-4,-5) a. Triangle B is the translation of triangle A 3 units to the right and 2 units down:  b. Triangle C is obtained by reflecting triangle A about the vertical axis:  c. Triangle D is obtained by stretching triangle A in both x- and y-direction by a factor of 2:  d. Triangle E is obtained by shifting triangle A 1 unit to the left and 2 units up:  e. Triangle F is obtained by reflecting triangle A about the vertical axis and then about the line y = x. Alternatively, it can also be obtained as a -90° rotation of triangle A about the origin (0,0).  f. Triangle G is obtained by reflecting triangle A about the horizontal axis and then about the line y = x. Alternatively, it can also be obtained as a 90° rotation of triangle A about the origin (0,0).    Problem H4 For example, (-2,3) becomes (-2,-3). In general, reflecting (x,y) about the horizontal axis yields (x,-y). In other words, the x-coordinate is unchanged while the y-coordinate is the negative of the original y-coordinate.   Problem H5 For example, (-2,3) becomes (2,3). In general, reflecting (x,y) about the vertical axis yields (-x,y). In other words, the y-coordinate is unchanged while the x-coordinate is the negative of the original x-coordinate.   Problem H6 For example (-2,3) becomes (3,-2). In general, if a point (x,y) is reflected about the line y = x, its new coordinates are (y,x). In other words, what used to be the x-coordinate becomes the y-coordinate, and what used to be the y-coordinate becomes the x-coordinate.     