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Pre-Calculus Homework Solutions 111

Pre-Calculus Homework Solutions 111 - 15 Use the origin as...

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15. • Use the origin as vertex Y of the triangle. • Place leg YZ of the triangle along the positive x -axis. • Position the triangle in the first quadrant. • Since X is on the y -axis, its x -coordinate is 0. Its y -coordinate is b because XY is b units long. • Since Z is on the x -axis, its y -coordinate is 0. Its x -coordinate is 2 b because XY b and ZY 2( XY ) or 2 b . 16. Since PQR is equilateral, the x -coordinate of R is halfway between 0 and 2 a , or a . So, the coordinates of R are ( a , b ). 17. Since LPQ is right isosceles, LP PQ and LP PQ . Then Q and P have the same x -coordinate, so the x -coordinate of P is a . P is on the x -axis, so its y -coordinate is 0. The distance from L to P is a units. The distance from P to Q must be the same. So, the coordinates of Q are ( a , a ) and the coordinates of P are ( a , 0). 18. JKN is isosceles, so JK JN . The distance from J to K is 2 a units. The distance from J to N must be the same. N is on the y -axis, so the coordinates of N are (0, 2 a ).
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