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Pre-Calculus Homework Solutions 113

# Pre-Calculus Homework Solutions 113 - 36 Sample answer X is...

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36. Sample answer: X is at the origin, so place Y ( a , b ) in the first quadrant. XYZ is scalene, so place Z on the x -axis so that the x -coordinate c is such that XZ YZ XY . So, the coordinates of Z are ( c , 0). 37. AB 4 a AC ¬ (0 ( 2 a )) 2 (2 a 0) 2 ¬ 4 a 2 4 a 2 or 8 a 2 CB ¬ (0 2 a ) 2 (2 a 0) 2 ¬ 4 a 2 4 a 2 or 8 a 2 Slope of AC 0 2 a ( 2 0 a ) or 1; slope of CB 2 0 a 2 a 0 or 1. AC CB and AC CB , so ABC is a right isosceles triangle. 38. Sample answer: Placing the figures on the coordinate plane is useful in proofs. We can use coordinate geometry to prove theorems and verify properties. Answers should include the following. • flow proof, two-column proofs, paragraph proofs, informal proofs, and coordinate proofs • Sample answer: The Isosceles Triangle Theorem can be proved using coordinate proof. 39. C; d ¬ ( 3 1) 2 [1 ( 2)] 2 ¬ 16 9 or 5 40. B; x 1 2 x 2 , y 1 2 y 2 5 2 ( 2) , 4 2 ( 1) ( 3.5, 1.5) Page 226 Maintain Your Skills 41. Given: 3 4 Prove: QR QS Proof: 42. Given: isosceles triangle JKN with vertex N , JK LM Prove: NML is isosceles Proof: 43. Given: AD CE , AD CE Prove:
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