Question

Решите задание номер не обижу но с пруфами​

Answer 1

$(0; 3,2);$

$(-6; 0);$

$(2; -1);$

$(0; 2);$

Пошаговое объяснение:

$y=kx+b;$

$A(-2; 4) \Rightarrow x=-2, \quad y=4; \quad B(3; 2) \Rightarrow x=3, \quad y=2;$

$$ \displaystyle \left \{ {{-2k+b=4} \atop {3k+b=2}} \right. \bigg |- \Leftrightarrow \left \{ {{-2k-3k+b-b=4-2} \atop {b=2-3k}} \right. \Leftrightarrow \left \{ {{-5k=2} \atop {b=2-3k}} \right. \Leftrightarrow \left \{ {{k=-0,4} \atop {b=3,2}} \right. ; $$

$y=kx+b \Rightarrow y=-0,4x+3,2;$

$y(0)=-0,4 \cdot 0+3,2=3,2;$

$AB \cap Oy=(0; 3,2);$

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$$ \displaystyle \left \{ {{-4k+b=2} \atop {-2k+b=4}} \right. \bigg | - \Leftrightarrow \left \{ {{-4k+2k+b-b=2-4} \atop {b=2+4k}} \right. \Leftrightarrow \left \{ {{-2k=-2} \atop {b=2+4k}} \right. \Leftrightarrow \left \{ {{k=1} \atop {b=6}} \right. ; $$

$y=x+6 \Rightarrow x+6=0 \Rightarrow x=-6;$

$AC \cap Ox=(-6; 0);$

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$$ \displaystyle \left \{ {{3k+b=2} \atop {k+b=-4}} \right. \bigg | - \Leftrightarrow \left \{ {{3k-k+b-b=2-(-4)} \atop {b=-k-4}} \right. \Leftrightarrow \left \{ {{2k=6} \atop {b=-k-4}} \right. \Leftrightarrow \left \{ {{k=3} \atop {b=-7}} \right. ; $$

$BE: \quad y=3x-7;$

$$ \displaystyle \left \{ {{-4k+b=2} \atop {4k+b=-2}} \right. \bigg | - \Leftrightarrow \left \{ {{-4k-4k+b-b=2-(-2)} \atop {b=-4k-2}} \right. \Leftrightarrow \left \{ {{-8k=4} \atop {b=-4k-2}} \right. \Leftrightarrow $$

$$ \displaystyle \Leftrightarrow \left \{ {{k=-\dfrac{1}{2}} \atop {b=0}} \right. ; $$

$CD: \quad y=-0,5x;$

$3x-7=-0,5x;$

$3x+0,5x=7;$

$3,5x=7;$

$x=2;$

$y(2)=-0,5 \cdot 2=-1;$

$BE \cap CD=(2; -1);$

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$$ \displaystyle \left \{ {{-2k+b=4} \atop {4k+b=-2}} \right. \bigg | - \Leftrightarrow \left \{ {{-2k-4k+b-b=4-(-2)} \atop {b=-4k-2}} \right. \Leftrightarrow \left \{ {{-6k=6} \atop {b=-4k-2}} \right. \Leftrightarrow $$

$$ \displaystyle \Leftrightarrow \left \{ {{k=-1} \atop {b=2}} \right. ; $$

$AD: \quad y=-x+2;$

$$ \displaystyle \left \{ {{-4k+b=2} \atop {3k+b=2}} \right. \bigg | - \Leftrightarrow \left \{ {{-4k-3k+b-b=2-2} \atop {b=2-3k}} \right. \Leftrightarrow \left \{ {{-7k=0} \atop {b=2-3k}} \right. \Leftrightarrow \left \{ {{k=0} \atop {b=2}} \right. ; $$

$CB: \quad y=2;$

$-x+2=2;$

$-x=2-2;$

$-x=0;$

$x=0;$

$y(0)=0+2=2;$

$AD \cap CB=(0; 2);$