Line segment AB has endpoints A(1, 4) and B(2, 8) . A dilation, centered at the origin, is applied to AB¯¯¯¯¯ . The image has endpoints A′(18, 12) and B′(14, 1) . What is the scale factor of the dilation? 1/8 1/2 2 8
To determine the scale factor of the dilation, we determine the distances between the endpoints of the two lines through the equation, d = √(x₂ - x₁)² + (y₂ - y₁)² Substituting the known values.
Line Segment 1: d = √(1 - 2)² + (4 - 8)² = 4.123
Line Segment 2: d = √(18 - 14)² + (12 - 1)² = 11.70
