Assuming the centre of dilation Q is the origin(0,0) If preimage U(x1,y1), then image U'(2.5x1, 2.5y1). The horizontal distance between U' and U would be dx=2.5x1-x1 = 1.5x1, the corresponding vertical distance is dy=2.5y1-y1 = 1.5y1 The oblique distance between U and U' is therefore x=sqrt(dx^2+dy^2)
Example: if U(2,3) is dilated about (0,0) with scale factor 2.5, U'(2.5*2, 2.5*3)=U'(5,7) Horizontal distance = (5-2)=3 Vertical distance = (7.5-3)=4.5 Oblique distance = sqrt(3^2+4.5^2)=sqrt(9+20.25)=sqrt(29.25)=5.41 approx.
If Q is NOT the origin, but Q(x0,y0) then U(x1,y1) U'(2.5(x1-x0)+x0,2.5(y1-y0)+y0) = U'(2.5x1-1.5x0, 2.5y1-1.5y0) The horizontal & vertical distances between U and U' is therefore dx=2.5x1-1.5x0-x1=1.5(x1-x0) dy=2.5y1-1.5y0-y1=1.5(y1-y0) The oblique distance between U and U' is therefore x=sqrt(dx^2+dy^2) =sqrt(1.5^2(x-x0)^2+1.5^2(y-y0)^2 =1.5sqrt((x-x0)^2+(y-y0)^2)
Example: U(5,5) dilated about (2,1) with scale factor of 2.5
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