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)