Question

find the image of (-1, 2) with respect to straight line 2x-3y+5=0​

Answer 1

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➠ Find the image of (-1, 2) with respect to straight line 2x-3y+5=0

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NOTE : There is mistake in question !

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Correct Question may be

• Find the image of (1,-2) with respect to straight line 2x-3y+5=0

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❏ Image of a point with respect to straight line means a point that lies at a same perpendicular distance from that line.

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❏ Here is the formula to find image of point P (h,k) about line ax + by + c = 0 where given point = (h,k) and image of that point = (x,y)

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$\boxed{\bold{ :\longmapsto \dfrac{x - h}{a} = \dfrac{y - k}{b} = -2\frac{(ah + bk + c)}{a^{2} +b^{2} } }}$

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$\underline{\boxed{\bold{ \bigstar \; Given \;\bigstar }}}$  

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➠ Given point : (1,-2)

➠ Equation of line : 2x - 3y + 5 =0

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$\underline{\boxed{\bold{ \bigstar \; Answer \; \bigstar }}}$  

Let's Start !

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Let's substitute values and simply to get our answer.

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$\boxed{\bold{ :\longmapsto \dfrac{x - h}{a} = \dfrac{y - k}{b} = -2\frac{(ah + bk + c)}{a^{2} +b^{2} } }}$

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$\bold{ :\implies \dfrac{x - 1}{2} = \dfrac{y - (-2)}{(-3)} = -2 \dfrac{ [2(1) -3(-2)+5]}{2^{2} +(3)^{2} } }$

$\bold{ :\implies \dfrac{x -1}{2} = \dfrac{y + 2}{(-3)} = -2 \dfrac{ [2 +6+5]}{4+9 } }$

$\bold { \orange { :\implies \dfrac{x -1}{2} = \dfrac{y - 2}{(-3)} = -2 \dfrac{ [13]}{13 } = -2 } }$

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Now let's find x-coordinate of image of given point.

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$\bold { :\implies \dfrac{x -1}{2} = -2 }$

$\bold { :\implies x -1 = -4 }$

$\bold { :\implies x = -4 + 1 }$

$\boxed { \bold { \red { :\leadsto x = -3 }}}$

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Now let's find y-coordinate of image of given point.

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$\bold { :\implies \dfrac{y +2}{-3} = -2 }$

$\bold { :\implies y +2 = 6 }$

$\bold { :\implies y = 6-2 }$

$\boxed { \bold { \red { :\leadsto y = 4 }}}$

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$\boxed{\boxed{\bold{\therefore Image \; of \; point (1,-2)\; w.r.t \;line \;2x - 3y + 5 = 0\; is\; point \; (-3,4) }}}$

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Hope this helps u.../

【Brainly Advisor】