**Unformatted text preview: **Geometry
Writing Assignment: Distance and Midpoint Formulas
Each problem is worth 5 points
Total Points: 50 Distance Formula
1. Find the distance between the points (-4, 6) and (8, -12).Round your solution to 2 decimal points.
d = √(x2-x1)^2 + (y2-y1)^2
√(8-(-4)^2 + (-12-(6))^2
= 2√79 - 17.77638883
= 17.78 2. Find the perimeter of the triangle below. Round your solution to 2 decimal points. d = √(x2-x1)^2 + (y2-y1)^2
dAC=√(3−(−3))^2+(2−6)^2
dAC=√(6)2+(−4)2
dAC=√36+16
dAC=√52
P = √52+ 6+4
P = √4*13+10
P = 10+7.21 = 17.21 dBC = √(3+3)^2+(2-2)^2
dBC = √36+0
dBC = 6 dAB = √(-3+3)^2+(2-6)^2
dAB = √(0)^2+(-4)^2
dAB = √16
dAB = 4 3. Find the length of diagonal XU in the hexagon below. Round your solution to 2 decimal points. U = (-2, 7)
X = (2, 2)
x1 = -2 x2 = 2
y1 =7 y2=2
(-2-2)^2/4^2 (-4)^2=16
16+25=41
Square root=6.40 4. Find the distance between the two points. Round your solution to 2 decimal points. d= √(4-(-5)^2 + (-1-(-2)^2
d= √(9)^2 + (1)^2
d= √81+1
d= √82
d= approximately 9.06 5. How much longer is CD compared to AB ? Round your solution to 2 decimal points. dCD= √(3-7)^2 +(2--2)^2
dCD= √(-4)^2 + (4)^2
dCD= √ 16 +16
dCD= √32
dCD= approximately 5.66 dAB= √(-8--11)^2 + (8-4)^2
dAB= √(3)^2 + (4)^2
dAB= √ 9 + 16
dAB= √ 25
dAB= 5.00
5.66-5.00 = 0.66 Midpoint Formula
6. Find the coordinates of the midpoint of AB . A (12, -7) and B (-4, 7).
M=(x1+x2/2 + y1+y2/2)
12+-4/2 + -7+7/2
=4
Midpoint = (4, 0) 7. M is the midpoint of JK . The coordinates of J are (6, 3) and the coordinates of M are (-3, 4), find the
coordinates of K.
(6+x)/2 + (3+y)/2)= (-3,4)
1/2( 6+x)=-3
6+x=-6
x=-12 1/2(3+y)=4
3+y=8y=5
K=(-12,5)
J=(6,3)
K=(-12,5) 8. Find the midpoint of TS . T(-6, 2) S(3, -4)
M=(x1+x2/2 + y1+y2/2)
(-6+3)/2 + (2+(-4))/2
Midpoint = (-3/2), -1 9. If the midpoint between (x, 6) and (-9, 14) is (8, 10), find the value of x.
M=(x1+x2/2 + y1+y2/2)
x1=x x2 = -9 y1= 6 y2= 14
x+(-9)/2 = 8
add two - x-9 = 16
add nine - x = 25 10. L is the midpoint of CD . If CL = 1
3 M=(x1+x2/2 + y1+y2/2)
(1/3)x + 8 = (2/3)x - 4
(1/3)x + 12 = (2/3)x
12 = (1/3)x
36 = x
CL = (1/3)36 + 8
CL = 12 + 8
CL = 20 x + 8 and LD = 2
3 x - 4 , find the length of CD . ...

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