calculate the vector
P1P2=(P2x−P1x;P2y−P1y)=(−3−2;−2−7)=(−5;−9)
let ax + by + c =0 is equation of the line
then direction vector is (b;-a) and coincides with the vector P1P2
hence b = -5
-a = -9
a = 9
9x- 5y + c = 0 equation of the line
h(ax+bx+c=0,(x0,y0))=a2+b2∣ax0+by0+c∣
where h is the distance from point to line
in our case h is equal to 2 and the coordinates of the point are equal to zero since they are the origin of coordinates
a2+b2∣ax0+by0+c∣=92+52∣c∣=106∣c∣
hence
c=2106 or c=−2106 and equation of the line
9x−5y+2106=0
or 9x−5y−2106=0
Answer: 9x−5y+2106=0 or 9x−5y−2106=0
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