Mathematics

# $2x+3y=7$ and $2x+3y=12$ are two parallel staright lines, then where does the point $(1,3)$ lies.

##### SOLUTION
Given: $2x+3y = 7$      $2x+3y=12$
Let $L_1 \to 2x+3y-7=0$           $L_2\to 2x+3y-12=0$
Let given point $P(1,3)$
If $L_1(P) \times L_2(P) < 0$  Point lies between lines
otherwise not between lies
$L_1 (P) = 2(1) + 3(3) - 7 = 4$
$L_2(P) = 2(1) + 3(3)-12 = -1$
$L_1(P) \times L_2(P) = 4 \times -1 = -4 < 0$
So point lies between the lines.

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Subjective Medium Published on 09th 09, 2020
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