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zhane2015
The endpoints of line AB A(9, 4) and B(5, –4). The endpoints of its image after a dilation are A'(6, 3) and B'(3, –3). What is the scale factor? Explain how you found your answer.
Point A: (9, 4) ==> (6, 3) The slope of the line it is traveling on is: m = (y1-y2) / (x1 - x2) = (4-3)/(9-6) = 1/3 and the equation for the line is: y - y0 = m(x - x0) y - 4 = (1/3)(x - 9) y = (1/3)(x - 9) + 4 y = (1/3)(x) - 3 + 4 y = (1/3)x +1 For Point B: (5, -4) ==> (3, -3) The slope of the line it is traveling on is: m = (y1-y2) / (x1 - x2) = (-4-(-3))/(5-3) = -1/2 and the equation for the line is: y - y0 = m(x - x0) y - (-4) = (-1/2)(x - 5) y + 4 = (-1/2)x + 5/2 y = (-1/2)x + 5/2 - 4 y = (-1/2)x + -3/2 To find the center, find the point of intersection: (1/3)x +1 = (-1/2)x + -3/2 2x + 6 = -3x -9 5x = -15 x = -15/5 x = -3 Then substitute into *either* equation: y = (1/3)x +1 y = (1/3)(-3) +1 y = -1 +1 y = 0 Center = (-3,0)