Pre-Calculus Homework Solutions 251

Pre-Calculus Homework Solutions 251 - slope of MR ¬ ( 4...

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Unformatted text preview: slope of MR ¬ ( 4 0)2 [ 3 ( 4)]2 ¬ 17 Since CD FG, CD FG. Next, use the Slope Formula to determine whether CD FG. FG y1 x1 23 3 ( 7) 1 4 3 ( 4) 40 1 4 ¬ ¬ slope of FG y ¬x slope of PR y 7 5 7 5 ( 4) ( 2) 4 2 ¬x y ¬x x 7 and y 3. slope of MR slope of NP y x y M ( 1) ( 1) 1 1 Move R: slope of MN ¬ ¬ CD and FG have the same slope, so they are parallel. Since one pair of opposite sides is congruent and parallel, CDFG is a parallelogram. 33. y ¬x Again, x 0 and y 9. So, move P to (0, 9). y2 x2 slope of CD slope of NP 8 1 8 1 6 ( 6) y6 x6 ¬3 1 ¬3 1 Again, x 7 and y 3. So, move R to ( 7, 3). 34. y Q Ox S N R W Sample answer: Hold N, P, and R fixed. Let M be M(x, y). Find the slopes of MN and MR so that they equal those of PR and NP, respectively. slope of MN slope of PR 1 1 1 1 y x y x 2 T Hold S, T, and W fixed. Let Q be Q(x, y). Find the slopes of QS and QW so that they equal those of TW and ST, respectively. slope of QS slope of TW ( 4) ( 2) ¬5 ¬ 23 1 4 1 4 1 4 If x 4 and y 1, then MN PR. slope of MR slope of NP 2 5 2 5 y x y x 4 ( 1) ( 1) ¬2 ¬3 1 6 x ( 6) y6 x6 y 1 5 1 5 1 5 ¬ 23 ¬ 32 4 6 ( 6) 8 1 Move P: slope of MN 1 x 0 and y ¬2 1 6 ( 6) 7 5 1 4 ¬3 5 ¬3 5 y x x 1 and y slope of QW Again, x 3 and y 4. So, move N to ( 3, 4). 1 y x y x y x y x ¬2 ( 2) ( 1) ¬ 41 y x ¬2 4 1 ¬5 ¬ 14 If x 0 and y 2, then QW ST. Move Q to (0, 2) to make both pairs of opposite sides parallel. Then QSTW is a parallelogram. Perform the same process for the other vertices. Move S: slope of QS slope of TW x 3 and y 4. slope of MR slope of NP 2 y x y x y x If x 0 and y 2, then QS TW. slope of QW slope of ST If x 4 and y 1, then MR NP. Move M to ( 4, 1) to make both pairs of opposite sides parallel. Then MNPR is a parallelogram. Perform the same process for the other vertices. Move N: slope of MN slope of PR 5 x O P 1 slope of PR 2 5 y ¬5 x 2y ¬5 x 3 ( 3) 4 2 3 ( 3) y3 x3 ¬ 41 ¬ 41 2. slope of ST 2 y ¬1 x 2y ¬1 x Again, x 1 and y 2. So, move S to (1, 2). 9. 253 Chapter 8 ...
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