If the points (1,2) and (3,4) lie on the same | vedclass

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(B) Let the line be $L(x, y) = 3x - 5y + a = 0$. The points $(x_1, y_1) = (1, 2)$ and $(x_2, y_2) = (3, 4)$ lie on the same side of the line if $L(x_1

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$R - (7, 11)$

Vedclass · Answer

(B) Let the line be $L(x, y) = 3x - 5y + a = 0$. The points $(x_1, y_1) = (1, 2)$ and $(x_2, y_2) = (3, 4)$ lie on the same side of the line if $L(x_1, y_1)$ and $L(x_2, y_2)$ have the same sign,i.e.,$L(x_1, y_1) \cdot L(x_2, y_2) > 0$.First,calculate $L(1, 2) = 3(1) - 5(2) + a = a - 7$.Second,calculate $L(3, 4) = 3(3) - 5(4) + a = a - 11$.For the points to be on the same side,$(a - 7)(a - 11) > 0$.Solving this inequality,we get $a  11$.Thus,$a \in (-\infty, 7) \cup (11, \infty)$,which is $R - [7, 11]$.

If the points $(1,2)$ and $(3,4)$ lie on the same side of the straight line $3x - 5y + a = 0$,then $a$ lies in the set

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