The points -x-1-y-1- and nbsp-x-2-y-2- lie on the same side of ax-by-c-0 if ax-1-by-1-c and nbsp-ax-2-by-2-c have the same sign-TrueFalse

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Standard XI

Mathematics

Relative Position of a Point with Respect to a Line

The points (x...

Question

The points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ lie on the same side of $a x + b y + c = 0$ if $a x_{1} + b y_{1} + c$ and $a x_{2} + b y_{2} + c$ have the same sign.

True

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False

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Similar questions

Show that the plane $a x + b y + c z + d = 0$ divides the line joining the points

$(x_{1}, y_{1}, z_{1}) a n d (x^{2}, y^{2}, z^{2})$ in the ratio

$- \frac{a x_{1} + b y_{1} + c z_{1} + d}{a x_{2} + b y_{2} + c z_{2} + d}$ .

Q. Show that the plane ax + by + cz + d = 0 divides the line joining the points (x₁, y₁, z₁) and (x₂, y₂, z₂) in the ratio

- \frac{a x_{1} + b y_{1} + c z_{1} + d}{a x_{2} + b y_{2} + c z_{2} + d}

Two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ lie on the same side of the straight line ax + by +c = 0 if ( $a x_{1} + b y_{1} + c$ ) ( $a x_{2} + b y_{2} + c$ ) is positive

Q. Statement 1: If the point

(2 a - 5, a^{2})

is on the same side of the line

x + y - 3 = 0

as that of the origin, then

a \in (2, 4) .

Statement 2: The point

(x_{1}, y_{1})

and

(x_{2}, y_{2})

lie on the same or opposite sides of the line

a x + b y + c = 0,

a x_{1} + b y_{1} + c

and

a x_{2} + b y_{2} + c

have the same or opposite signs.

Q. The plane

P; a x + b y + c z + d = 0

divides the line joining

(x_{1}, y_{1}, z_{1})

and

(x_{2}, y_{2}, z_{2})

in the ratio of

(- \frac{{a x}_{1} + {b y}_{1} + {c z}_{1} + d}{{a x}_{2} + {b y}_{2} + {c z}_{2} + d}) = - \frac{p_{1}}{p_{2}}

; where

P_{1} = {a x}_{1} + {b y}_{1} + {c z}_{1} + d

and

P_{2} = {a x}_{2} + {b y}_{2} + {c z}_{2} + d

. If true enter 1 else 0

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The points (x1,y1) and (x2,y2) lie on the same side of ax+by+c=0 if ax1+by1+c and ax2+by2+c have the same sign.

The points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ lie on the same side of $a x + b y + c = 0$ if $a x_{1} + b y_{1} + c$ and $a x_{2} + b y_{2} + c$ have the same sign.