Question

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

Answer 1

The answer is 1/8!

Explanation:

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Answer 2

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

Dividing the answers will give us 0.352