Question 140

The distance between the lines $$\frac{x}{3} + \frac{y}{4} = 1$$ and 8x + 6y = 5 in units, is

we know the fourmula of distance between two lineΒ 

$$(A_{1}x +B_{1}y +C)\div\\sqrt({A_{1}^{2}+B_{1}^{2}})$$ = $$\pm$$Β $$(A_{2}x +B_{2}y +C)\div\\sqrt({A_{2}^{2}+B_{2}^{2}})$$

then we have hereΒ  $$(A_{1}$$Β = 1\3Β Β $$(B_{1}$$ = 1\4 andΒ $$(c_{1}$$ = -1 andΒ 

Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β $$(A_{2}$$ = 8 $$(B_{2}$$ = 8Β  and $$(c_{2}$$ = -5Β 

thenΒ 

|$$(A_{1}x +B_{1}y +C)\div\\sqrt({A_{1}^{2}+B_{1}^{2}})$$| = $$\pm$$ |$$(A_{2}x +B_{2}y +C)\div\\sqrt({A_{2}^{2}+B_{2}^{2}})$$|

|$$\frac{1\3 + 1\4Β - 1}\sqrt{{1\3}^{2}+{1\4}^{2}}$$| = $$\pm$$ |$$\frac{8 +6 -5}\sqrt{{8}^{2}+{6}^{2}}$$|

1 + 9\10 = 10\19Β  AnswerΒ 

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