Question

Se considera punctele A(1;-1),B(-1;3) si dreapta d: 5x-12y-1=0. Sa se determine distanta de pa punctul M, mijlocul segmentului [AB],la dreapta d.

Answer 1

$Punctul\;M\;are\;coordonatele:\\\\M(x_M,y_M)=M\left(\dfrac{x_A+x_B}{2},\dfrac{y_A+y_B}{2}\right)=M\left(\dfrac{1-1}{2},\dfrac{-1+3}{2}\right)=M(0,1).\\\\Distan\c{t}a\ de\ la\ punctul\;M\;la\;dreapta\;d\;este:\\\\d(M,d)=\dfrac{|5\cdot x_M-12\cdot y_M-1|}{\sqrt{5^2+(-12)^2}}=\dfrac{|5\cdot 0-12\cdot 1-1|}{\sqrt{25+144}}=\dfrac{|-13|}{13}=1.$

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