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Geo I HW 1-14 Name _________________ Date _____________ A is the midpoint of segment JM. JA = 6x AM = 4y + 2 JM = 4x + 6y 1. Draw and label a picture to represent this situation. J 6x A 4y + 2 M 4x + 6y 2. Set up a system of equations to solve for x and y. 6x = 4y + 2 6x + 4y + 2 = 4x + 6y 6x – 4y = 2 2x – 2y = -2 Other equation options include: 2 2 2(6x) = 4x + 6y 2(4y + 2) = 4x + 6y 12x = 4x + 6y 8y + 4 = 4x + 6y 3x – 2y = 1 x – y = -1 8x – 6y = 0 -4x + 2y = -4 3. Solve the system for x and y. Then find JM. Elimination, cancelling the x’s Elimination, cancelling the y’s 3x – 2y = 1 -3(x – y = -1) 3x – 2y = 1 -2(x – y = -1) 3x – 2(4) = 1 3x – 8 = 1 3x = 9 x=3 3x – 2y = 1 -3x + 3y = 3 y=4 3(3) – 2y = 1 9 – 2y = 1 -2y = -8 y=4 3x – 2y = 1 -2x + 2y = 2 x =3 Substitution x – y = -1 x=y–1 x=4–1 x=3 3x – 2y = 1 3(y – 1) – 2y = 1 3y – 3 – 2y = 1 y–3=1 y=4 JM = 4x + 6y = 4(3) + 6(4) = 12 + 24 = 36 JA = 6x = 6(3) = 18 AM = 4y + 2 = 4(4) + 2 = 16 + 2 = 18 IE bisects FIR. RIE = 2x – 8 FIR = 3x + 9 4. Draw and label a picture to represent this situation. F I 3x + 9 E R 5. Set up an equation and solve for x. 2(2x – 8 ) = 3x + 9 4x – 16 = 3x + 9 x = 25 A B C 1 3 2 D 6. What does the Segment Addition Postulate tell you about this diagram? AB + BC = AC 7. What does the Vertical Angle Thm tell you about this diagram? 1 3 8. What does the Angle Addition Postulate tell you about this diagram? 1 + 2 = DCA 9. The sum of an angle’s supplement and 7 times its complement is 10 less than twice the angle. Find the measure of the angle’s complement. 180 – x + 7(90 – x) = 2x – 10 180 – x + 630 – 7x = 2x – 10 810 – 8x = 2x – 10 -10x = -820 x = 82 complement = 90 – 82 = 8 10. Find the midpoint of segment YZ. Y(5, 8) Z(-7, 13) x-coordinate: -7 + 5 = -2 = -1 2 2 y-coordinate: 8 + 13 = 21 = 10½ 2 2 Midpoint is (-1, 10½)