Pre-Calculus Homework Solutions 169

# Pre-Calculus Homework Solutions 169 - 30 Use the Distance...

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Unformatted text preview: 30. Use the Distance Formula to find DE and AB. 26. In order to show QT RS, we must show that PQ QR PQ QR PT TS PT TS . ¬ 34.88 or 436 18.32 229 33.25 11.45 ¬ 11.45 21.8 ¬ 11.45 or 436 229 PQ PT 436 Thus, QR TS 229 . Since the sides have y A 4 x 8 B DE ¬3 2 , 26 3 2 4 1 2 2 81 4 10 31. y C 1 2 AB. A (2, 12) (5, 17). 20 C ¬ [ 4 ( 1)]2 ( 3 6)2 ¬ 9 81 ¬3 10 So, 3 10 1 (3 10) and thus DE 2 2 slope of TS Because the slopes of WM and TS are equal, WM TS. WM is a midsegment of RST if W is the midpoint of RT and M is the midpoint of RS. 11 8 4 AB 12 14 5 3 or 1 20 26 17 11 or 1 2 3 2 ¬ ¬9 4 28. If the slopes of WM and TS are equal, WM TS. 1 8 8 27. DE is a midsegment of ABC and DE BC, so by the Triangle Midsegment Theorem, DE 1 BC. 2 Then BC 2DE. DE ¬ (4 1)2 (3 1)2 ¬9 4 ¬ 13 BC ¬2DE ¬2 13 ¬ 4 13 or 52 The midpoint of RT is 4 4 proportional lengths, QT RS. slope of WM 8 (8, 14). 2 These are not the coordinates of W. 17 8 1 The midpoint of RS is , 2 2 D These are not the coordinates of M. WM is not a midsegment because W and M are not midpoints of their respective sides. y 8 4 x 8 4 4 B 8 4 C 8 D 1 76 2, E 47 2, ( 5) 2 3 x Graph AB. We can find segments of AB with lengths in a ratio of 2 to 1 by considering a second line and parallel lines that intersect this line and AB. Graph C(0, 12) and D(0, 0) and lines CA and DB. CA and DB are horizontal lines and are parallel lines intersecting transversals CD (the y-axis) and AB. We can find P by finding a third parallel line intersecting CD and AB so that this line separates CD into two parts with a ratio of 2 to 1. CD is 12 units, so if a horizontal line intersects CD at (0, 4) or (0, 8) then this line separates CD into two parts with a ratio of 2 to 1. These horizontal lines intersect AB at (4, 4) and (3, 8). These points cut off AB into parts with a ratio of 2 to 1, so P could have coordinates (4, 4) or (3, 8). 29. DE is a midsegment of ABC. Use the Midpoint Formula to find the coordinates of D and E. A B (5, 0) D 3, 1 2 ( 5) E 3, 2 2 4 Find the slopes of DE and AB. slope of DE slope of AB 4 3 2 or 3 3 3 4 1 2 6 ( 1) or 3 Both DE and AB have slope 3, so DE is parallel to AB. 171 Chapter 6 ...
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## This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.

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