Nadine A

21 November 2023 09:55

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Nadine A

21 November 2023 09:55

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11 Desember 2023 02:25

<p>Yuks mari kita bahas.....</p><p>&nbsp;</p><p>2. a. Garis 2y + 5x = 10</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; a = 5, b = 2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; m = -a/b = -5/2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; "<strong>Dua garis saling sejajar maka gradiennya sama"</strong></p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Persamaan garis melalui (2,-3) dengan gradien (m) = -5/2 adalah</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y - y₁ = m(x - x₁)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y + 3 = -5/2(x - 2)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y + 3 = -5/2 x + 5</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y = -5/2 x + 5 -3</p><p>&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<strong> y = -5/2 x + 2</strong></p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;atau</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2y = -5x + 4 &nbsp; &nbsp; (dikalikan 2)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<strong>5x + 2y - 4 = 0</strong></p><p>&nbsp;</p><p>&nbsp; &nbsp;b. Persamaan garis yang tegak lurus dengan 2y + 5x = 10 dan&nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp; melalui (2,-3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp;"<strong>Dua garis saling tegak lurus maka m<sub>1</sub> x m<sub>2</sub> = -1</strong>"</p><p>&nbsp; &nbsp; &nbsp; &nbsp; -5/2 x m<sub>2</sub> = -1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; m<sub>2</sub> = 2/5</p><p>&nbsp; &nbsp; &nbsp; &nbsp; Persamaan garis melalui (2,-3) dengan m = 2/5</p><p>&nbsp; &nbsp; &nbsp; &nbsp; y - y₁ = m(x - x₁)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; y + 3 = 2/5(x - 2)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; y + 3 = 2/5 x - 4/5</p><p>&nbsp; &nbsp; &nbsp; &nbsp; 5y + 15 = 2x - 4 &nbsp; &nbsp; &nbsp;(dikalikan dengan 5)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; 2x - 5y - 4 - 15 = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<strong>2x - 5y - 19 = 0</strong></p><p>&nbsp;</p><p>3. a. Gradien (m) garis yang melalui ( 4,-5) dan (-3,6)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (4, -5) = (x<sub>1</sub>,y<sub>1</sub>)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (-3, 6) = (x<sub>2</sub>,y<sub>2</sub>)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; m = (y<sub>2</sub> - y<sub>1</sub>)/(x<sub>2 </sub>- x<sub>1</sub>)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= (6 + 5)/(-3 - 4)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= -11/7</p><p>&nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; "<strong>Dua garis saling sejajar maka gradiennya sama"</strong></p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Persamaan garis melalui (3,2) dengan gradien (m) = -11/7 adalah</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y - y₁ = m(x - x₁)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y - 2 = -11/7(x - 3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y - 2 = -11/7 x + 33/7 &nbsp; &nbsp; &nbsp; (dikalikan 7 supaya pecahan hilang)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;7y - 14 = -11x + 33</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;11x + 7y - 14 - 33 = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<strong>11x + 7y - 47 = 0</strong></p><p>&nbsp; &nbsp; &nbsp;&nbsp;</p><p>&nbsp; &nbsp;b. Persamaan garis yang tegak lurus dengan ( 4,-5) dan (-3,6) dan&nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp; melalui (3,2)</p><p>&nbsp; &nbsp; &nbsp; &nbsp;"<strong>Dua garis saling tegak lurus maka m<sub>1</sub> x m<sub>2</sub> = -1</strong>"</p><p>&nbsp; &nbsp; &nbsp; &nbsp; -11/7 x m<sub>2</sub> = -1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; m<sub>2</sub> = 7/11</p><p>&nbsp; &nbsp; &nbsp; &nbsp; Persamaan garis melalui (3,2) dengan m = 7/11</p><p>&nbsp; &nbsp; &nbsp; &nbsp; y - y₁ = m(x - x₁)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; y - 2 = 7/11(x - 3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; y - 2 = 7/11 x - 21/11 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (dikalikan 11 supaya pecahan hilang)</p><p>&nbsp; &nbsp; &nbsp; &nbsp;11y - 22 = 7x - 21</p><p>&nbsp; &nbsp; &nbsp; &nbsp;7x - 11y - 21 + 22 = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp;<strong>7x - 11y + 1 = 0</strong></p><p>&nbsp;</p>

Yuks mari kita bahas.....

 

2. a. Garis 2y + 5x = 10

          a = 5, b = 2

          m = -a/b = -5/2

          "Dua garis saling sejajar maka gradiennya sama"

         Persamaan garis melalui (2,-3) dengan gradien (m) = -5/2 adalah

         y - y₁ = m(x - x₁)

         y + 3 = -5/2(x - 2)

         y + 3 = -5/2 x + 5

         y = -5/2 x + 5 -3

         y = -5/2 x + 2

         atau

         2y = -5x + 4     (dikalikan 2)

         5x + 2y - 4 = 0

 

   b. Persamaan garis yang tegak lurus dengan 2y + 5x = 10 dan 

        melalui (2,-3)

       "Dua garis saling tegak lurus maka m1 x m2 = -1"

        -5/2 x m2 = -1

        m2 = 2/5

        Persamaan garis melalui (2,-3) dengan m = 2/5

        y - y₁ = m(x - x₁)

        y + 3 = 2/5(x - 2)

        y + 3 = 2/5 x - 4/5

        5y + 15 = 2x - 4      (dikalikan dengan 5)

        2x - 5y - 4 - 15 = 0

        2x - 5y - 19 = 0

 

3. a. Gradien (m) garis yang melalui ( 4,-5) dan (-3,6)

          (4, -5) = (x1,y1)

          (-3, 6) = (x2,y2)

          m = (y2 - y1)/(x2 - x1)

               = (6 + 5)/(-3 - 4)

               = -11/7

 

          "Dua garis saling sejajar maka gradiennya sama"

         Persamaan garis melalui (3,2) dengan gradien (m) = -11/7 adalah

         y - y₁ = m(x - x₁)

         y - 2 = -11/7(x - 3)

         y - 2 = -11/7 x + 33/7       (dikalikan 7 supaya pecahan hilang)

         7y - 14 = -11x + 33

         11x + 7y - 14 - 33 = 0

         11x + 7y - 47 = 0

      

   b. Persamaan garis yang tegak lurus dengan ( 4,-5) dan (-3,6) dan 

        melalui (3,2)

       "Dua garis saling tegak lurus maka m1 x m2 = -1"

        -11/7 x m2 = -1

        m2 = 7/11

        Persamaan garis melalui (3,2) dengan m = 7/11

        y - y₁ = m(x - x₁)

        y - 2 = 7/11(x - 3)

        y - 2 = 7/11 x - 21/11           (dikalikan 11 supaya pecahan hilang)

       11y - 22 = 7x - 21

       7x - 11y - 21 + 22 = 0

       7x - 11y + 1 = 0

 


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