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 = √ (x1 - x2)² + (y1 - y2)
d = √ (-4 - 8)² + (6 - -12)²
d = √ (-12)² + (18)²
d = √ (144) + (324)
d = √ 468
d = 21.63 2. Find the perimeter of the triangle below. Round your solution to 2 decimal points. Point A is 4 units above Point B.
Point C is 4 units right of Point B.
Distance between Point A and Point C:
d = √ (x1 - x2)² + (y1 - y2)²
d = √ (-3 - 3)² + (6 - 2)²
d = √ (-6)² + (4)²
d = √ (36) + (16)
d = √ (52)
d = 7.21
Perimeter = 4 + 4 + 7.21 = 15.21 units 3. Find the length of diagonal XU in the hexagon below. Round your solution to 2 decimal points. X(2,2) U(-2,7)
d = √ (2 - -2)² + (2 - 7)²
d = √ (16) + (25)
d = √ 41 = 6.40 units 4. Find the distance between the two points. Round your solution to 2 decimal points. d = √ (x1 - x2)² + (y1 - y2)²
d = √ (-5 - 4)² + (-2 - -1)²
d = √ (-9)² + (-1)²
d = √ (81) + (1)
d = √ 82
d = 9.06 5. How much longer is CD compared to AB ? Round your solution to 2 decimal points. d = √ (-11 - -8)² + (4 - 8)²
d = √ (-3)² + (-4)²
d = √ (9) + (16) = √25 = 5 (5.66) - (5) = 0.66
CD is about 0.66 units longer than AB. d = √ (3 - 7)² + (2 - -2)²
d = √ (-4)² + (4)²
d = √ (16) + (16) = √32 = 4√2 = 5.66 Midpoint Formula
6. Find the coordinates of the midpoint of AB . A (12, -7) and B (-4, 7).
( (x1 + x2)/2 ) , ( (y1 + y2)/2 ) = M
( (12 + -4)/2 ) , ( (-7 + 7)/2 ) = M
( (8)/2 ) , ( (0)/2 ) = M
(4),(0)=M
(4,0) = M
midpoint of AB is located at (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.
( (x1 + x2)/2 ) , ( (y1 + y2)/2 ) = M
( (6 + x1)/2 ) , ( (3 + y2)/2 ) = (-3,4)
(6+x2)/2 = -3
(3+y2)/2 = 4
6+x2 = -6
3+y2 = 8
x2 = -12
y2 = 5
K(-12,5) 8. Find the midpoint of TS . ( (x1 + x2)/2 ) , ( (y1 + y2)/2 ) = M
( (-6 + 3)/2 ) , ( (2 + -4)/2 ) = M
( (-3)/2 ) , ( (-2)/2 ) = M
( -1.5 ) , ( -1 ) = M
M (-1.5,-1)
Midpoint of TS is located at (-1.5,-1) 9. If the midpoint between (x, 6) and (-9, 14) is (8, 10), find the value of x.
( (x1 + x2)/2 ) , ( (y1 + y2)/2 ) = M
( (x + -9)/2 ) , ( (6 + 14)/2 ) = (8, 10)
(x + -9)/2 = 8
x + -9 = 16
x = 25 10. L is the midpoint of CD . If CL = 1 x + 8 and LD = 3 (1/3)x + 8 = (2/3)x - 4
8 = (1/3)x - 4
36 = x
CD = CL + LD = (1/3)x + 8 + (2/3)x - 4
CD = (1/3)(36) + 8 + (2/3)(36) - 4
CD = 12 + 8 + 24 - 4
CD = 40 2
3 x - 4 , find the length of CD . ...
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