समान्तर रेखाएँ 3x + 4y = 5 तथा 6x + 8y = 45 के बीच की दूरी ज्ञात कीजिए।
Answers
Answer:
answer of this question is 9
Given : समान्तर रेखाओं 3x + 4y = 5 और 6x + 8y = 45
parallel lines 3x + 4y = 5 and 6x + 8y = 45
To Find : समान्तर रेखाओं 3x + 4y = 5 और 6x + 8y = 45 के बीच की दूरी
Distance between parallel lines
Solution :
3x + 4y = 5
6x + 8y = 45
Slope of the line = - 3/4
Hence Slope of perpendicular line = 4/3
Let say a line y = 4x/3 cuts both the line
3x + 4y = 5
=> 3x + 4(4x/3) = 5
=> 9x + 16x = 15
=> 25x = 15
=> x = 3/5
y = 4/5
6x + 8y = 45
=> 6x +8(4x/3) = 45
=> 18x + 32x = 135
=> 50x = 135
=> 10x = 27
=> x = 27/10
y = 36/10
Points are ( 3/5 , 4/5) and ( 27/10 , 36/10)
Distance = √(27/10 - 3/5)² + (36/10 - 4/5)²
= (1/10)√ 21² + 28²
= (7/10)√3² + 4²
= (7/10)5
= 35/10
= 3.5
समान्तर रेखाओं 3x + 4y = 5 और 6x + 8y = 45 के बीच की दूरी = 3.5
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