SBMPTN Zone : Refleksi (Pencerminan)

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Tipe:

Standar SBMPTN HOTS

No.

Hasil pencerminan titik A (1, -2) terhadap garis {ax + by + 2 = 0} adalah A'(3, 4). Nilai {a + b} adalah

1. -\dfrac65
2. \dfrac25
3. -\dfrac25

4. \dfrac85
5. -\dfrac85

SKMP September 2020

Titik tengah A dan A'
B\left(\dfrac{1+3}2,\dfrac{-2+4}2\right)=B(2,1)

B dilalui oleh garis {ax + by + 2 = 0}
$$\begin{array}{rl}2a+b+2& =0\\ 2a+b& =-2\end{array}$$

Gradien garis AA'
$$\begin{array}{rl}{m}_{A{A}^{\prime }}& ={\displaystyle \frac{y_{A^{\prime }}-y_A}{x_{A^{\prime }}-x_A}}\\ & ={\displaystyle \frac{4-(-2)}{3-1}}\\ & ={\displaystyle \frac{6}{2}}\\ & =3\end{array}$$

gradien garis {ax + by + 2 = 0}
$$\begin{array}{rl}m& =-{\displaystyle \frac{1}{m_{A{A}^{\prime }}}}\\ -{\displaystyle \frac{a}{b}}& =-{\displaystyle \frac{1}{3}}\\ {\displaystyle \frac{a}{b}}& ={\displaystyle \frac{1}{3}}\\ b& =3a\end{array}$$

$$\begin{array}{rl}2a+b& =-2\\ 2a+3a& =-2\\ 5a& =-2\\ a& =-{\displaystyle \frac{2}{5}}\end{array}$$

$$\begin{array}{rl}a+b& =a+3a\\ & =4a\\ & =4(-{\displaystyle \frac{2}{5}})\\ & =\boxed{{\displaystyle \boxed{{\displaystyle -{\displaystyle \frac{8}{5}}}}}}\end{array}$$

Jadi, {a + b=-\dfrac85}. JAWAB: E