13.
You start walking from the origin in the direction of (3,1), with the intention of
ending at point (7,1). You are allowed one right-angle turn. Find (a) the point at
winich you make this turn, (b) how far you walked in the (3,1) direction, and (c)
how far you walked orthogonal to the (3,1) direction.
Answers
Given : You start walking from the origin in the direction of (3,1), with the intention of ending at point (7,1). You are allowed one right-angle turn.
To find : (a) the point at winich you make this turn, (b) how far you walked in the (3,1) direction, and (c) how far you walked orthogonal to the (3,1) direction.
Solution:
Started from origin (0 , 0) to direction ( 3 , 1)
Hence Slope = 1/3
line y - 0 = (1/3)(x - 0)
=> y = x/3
=> x = 3y
Lets Say point is ( 3a , a ) at which right angle turn is made
Slope between (3a , a) & (7 , 1) will be -1/(1/3) = - 3
=> (a - 1)/(3a - 7) = - 3
=>a - 1 = -9a + 21
=> 10a = 22
=> a = 22/10
a = 11/5
3a = 33/5
Point ( 33/5 , 11/5) or ( 6.6 , 2.2) at which turn taken
Walked in direction, of ( 3 , 1)
= √(33/5 -0 )² + (11/5 - 0)² = (11/5) √9 + 1 = 11√10/5
11√10/5 = 6.957
walked orthogonal to the (3,1) direction.
= √(33/5 - 7)² + (11/5 - 1)²
= √(2/5)² + (6/5)²
= (2/5) √ 1 + 9
= 2√10/5 = 1.265
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