= 1 Equation of a straight line path is 2x + y = 12. A man is standing at a point (2,3). He wants to reach the straight line path in least time. Based on the above information, answer the following questions 1. the slope of the path followed by the man is ( (a) (b) - (c) 2 (d) —2 2 2. equation of the path followed by the man is (a) 2x + y = 4 (b) 2x - y + 4 = 0 (c) x - 2y + 4 = 0 (d) x + 2y +4 = 0
Answers
Given : Equation of a straight line path is 2x+y-12-0. A man is standing at a point (2,3). He wants to reach the straight line path in least possible time.
To Find : The slope of the path followed by man
Equation of the path followed by man
additional Questions: from https://brainly.in/question/47813282
Coordinates of point where path followed by man and given straight Line path meet
The distance covered by man in reaching the straight line path
Solution:
path is 2x+y-12-0
y = - 2x + 12
Comparing with y = mx + c
m = - 2
Hence slope of the path = - 2
Perpendicular Distance is shortest distance
Hence path followed by man would be perpendicular
and Product of slope of perpendicular lines is - 1
Hence - 2 * m = - 1
=> m = 1/2
. The slope of the path followed by man is 1/2
Man was at (2 , 3) and slope = 1/2
Equation of the path followed by man
y - 3 = (1/2) (x - 2)
=> 2y - 6 = x - 2
=> x - 2y + 4 = 0
2x+y-12-0 , x - 2y + 4 = 0
On solving x = 4 , y = 4
. Coordinates of point where path followed by man and given straight Line path meet is ( 4 , 4)
The distance covered by man = Distance between (2 ,3 ) and ( 4 , 4)
= √(4 - 2)² + (4 - 3)²
= √4 + 1
= √5 unit
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Answer:
path is 2x+y-12-0
y = - 2x + 12
Comparing with y = mx + c
m = -2
Hence slope of the path=-2.
Perpendicular Distance is shortest distance
Hence path followed by man would be perpendicular
and Product of slope of perpendicular lines is - 1
Hence -2* m = -1.
=> m = 1/2
. The slope of the path followed by man is
1/2
Man was at (2, 3) and slope = 1/2
y - 3=(1/2) (x - 2)
Equation of the path followed by man => x - 2y + 4 = 0
=> 2y - 6 = x -2
2x+y-12-0
x - 2y + 4 = 0
On solving x = 4, y = 4
Coordinates of point where path followed by man and given straight Line path meet is (4,4)
The distance covered by man = Distance between (2,3) and (4,4)
= √(4- 2)² + (4 - 3)²
= √4 +1
= √5 unit.
