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Reycha A

23 November 2023 14:39

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Reycha A

23 November 2023 14:39

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Sumara S

24 November 2023 13:32

<p>diketahui y = x<sup>2</sup> + 6</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; faktor skala = <sup>1</sup>/<sub>3</sub></p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; titik pusat P(6,-3)</p><p>ditanya persamaan bayangan kurva...?</p><p>lesaian:</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(x') = (<sup>1</sup>/<sub>3</sub> &nbsp; &nbsp;0 &nbsp; )(x - 6) + ( 6 )</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(y') &nbsp; &nbsp;( 0 &nbsp; &nbsp; &nbsp;<sup>1</sup>/<sub>3 </sub>)(y + 3) &nbsp; &nbsp;(-3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; x - 6 &nbsp; &nbsp; &nbsp; &nbsp; 18 &nbsp; &nbsp; &nbsp; &nbsp;x + 12</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; x' &nbsp;= ------- + &nbsp;----- = &nbsp; --------&nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 3 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 3</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &lt;=&gt; 3x' = x + 12</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &lt;=&gt; x = 3x' - 12</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; y + 3 &nbsp; &nbsp; &nbsp; &nbsp;9 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; y - 6</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; y' &nbsp;= ------- - &nbsp;----- = &nbsp; --------</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 3</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &lt;=&gt; 3y' = y - 6</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &lt;=&gt; y = 3y' + 6</p><p>persamaan kurva y = x<sup>2</sup> + 6</p><p>persamaan bayangannya:</p><p>y = x<sup>2</sup> + 6</p><p>3y' + 6 = (3x' - 12)<sup>2</sup> + 6</p><p>3y' + 6 = 9x'<sup>2</sup> - 24x' + 2 + 6</p><p>3y' = 9x'<sup>2</sup> - 24x' + 2</p><p>3y = 9x<sup>2</sup> - 24x + 2</p><p>jadi persamaan bayangannya 3y = 9x<sup>2</sup> - 24x + 2</p><p>semoga membantu.</p>

diketahui y = x2 + 6

                      faktor skala = 1/3

                      titik pusat P(6,-3)

ditanya persamaan bayangan kurva...?

lesaian:

                   (x') = (1/3    0   )(x - 6) + ( 6 )

                   (y')    ( 0      1/3 )(y + 3)    (-3)

                                x - 6         18        x + 12

                      x'  = ------- +  ----- =   -------- 

                                   3             3             3

              <=> 3x' = x + 12

              <=> x = 3x' - 12

                                y + 3        9           y - 6

                      y'  = ------- -  ----- =   --------

                                   3            3             3

              <=> 3y' = y - 6

              <=> y = 3y' + 6

persamaan kurva y = x2 + 6

persamaan bayangannya:

y = x2 + 6

3y' + 6 = (3x' - 12)2 + 6

3y' + 6 = 9x'2 - 24x' + 2 + 6

3y' = 9x'2 - 24x' + 2

3y = 9x2 - 24x + 2

jadi persamaan bayangannya 3y = 9x2 - 24x + 2

semoga membantu.

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