(C) Let the given line be $L(x, y) = 7x + 5y - 9 = 0$. Substitute the first point $(3, 4)$ into the expression: $L(3, 4) = 7(3) + 5(4) - 9 = 21 + 20 -

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(C) Let the given line be $L(x, y) = 7x + 5y - 9 = 0$. Substitute the first point $(3, 4)$ into the expression: $L(3, 4) = 7(3) + 5(4) - 9 = 21 + 20 - 9 = 32$. Since $32 > 0$,the point $(3, 4)$ lies on the positive side of the line. Substitute the second point $(-9, 6)$ into the expression: $L(-9, 6) = 7(-9) + 5(6) - 9 = -63 + 30 - 9 = -42$. Since $-42 Because the values have opposite signs,the points lie on opposite sides of the line.

Class 11 Mathematics Straight Line Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

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On which side of the line $7x + 5y - 9 = 0$ do the points $(3, 4)$ and $(-9, 6)$ lie?

A
Same side
B
Origin side
C
Opposite sides
D
Adjacent sides

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Straight Line

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Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

The vertices of $\Delta OBC$ are $(0, 0)$,$(-3, 1)$,and $(-1, -3)$ respectively. $A$ line parallel to $BC$ intersects $OB$ and $OC$ at a distance of $1/2$ from $O$. Find the equation of this line.

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The position of the point $(8, -9)$ with respect to the lines $2x + 3y - 4 = 0$ and $6x + 9y + 8 = 0$ is

Easy

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The positions of the points $(3, 4)$ and $(2, -6)$ with respect to the line $3x - 4y = 8$ are:

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The vertices of a triangle $OBC$ are $(0,0)$,$(-3,-1)$,and $(-1,-3)$ respectively. The equation of the line parallel to $BC$ which is at a distance of $\frac{1}{2}$ unit from the origin and cuts $OB$ and $OC$ is:

MediumIIT 1976

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The base of an equilateral triangle is along the line given by $3x + 4y = 9$. If a vertex of the triangle is $(1, 2)$,then the length of a side of the triangle is

DifficultJEE MAIN 2014

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On which side of the line $7x + 5y - 9 = 0$ do the points $(3, 4)$ and $(-9, 6)$ lie?

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The vertices of $\Delta OBC$ are $(0, 0)$,$(-3, 1)$,and $(-1, -3)$ respectively. $A$ line parallel to $BC$ intersects $OB$ and $OC$ at a distance of $1/2$ from $O$. Find the equation of this line.

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