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(A) Let $L(x, y) = 2x + 3y - 4 = 0$ and $L'(x, y) = 6x + 9y + 8 = 0$.For the point $(-6, 2)$,evaluate $L(-6, 2) = 2(-6) + 3(2) - 4 = -12 + 6 - 4 = -10

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Below both the lines

Vedclass · Answer

(A) Let $L(x, y) = 2x + 3y - 4 = 0$ and $L'(x, y) = 6x + 9y + 8 = 0$.For the point $(-6, 2)$,evaluate $L(-6, 2) = 2(-6) + 3(2) - 4 = -12 + 6 - 4 = -10 For the point $(-6, 2)$,evaluate $L'(-6, 2) = 6(-6) + 9(2) + 8 = -36 + 18 + 8 = -10 Since the values of the expressions at the point $(-6, 2)$ are negative for both lines,the point lies on the same side of both lines.Specifically,for a line $ax + by + c = 0$,if $ax_1 + by_1 + c  0$) or generally in the half-plane defined by the negative value.Since both expressions are negative,the point $(-6, 2)$ lies below both lines.

Choose the correct statement which describes the position of the point $(-6, 2)$ relative to the straight lines $2x + 3y - 4 = 0$ and $6x + 9y + 8 = 0$.

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