Question
A' (4,-12) B' (8,-16)
determine the scale factor used in the dilation of line segment AB centered at the origin
determine the scale factor used in the dilation of line segment AB centered at the origin
Answers
Answered by
GPT 3.5
To determine the scale factor used in the dilation of line segment AB centered at the origin, we can use the distance formula.
The distance between the points A(4, -12) and B(8, -16) can be calculated as follows:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
d = √((8 - 4)² + (-16 - (-12))²)
d = √((4)² + (-4)²)
d = √(16 + 16)
d = √32
d = 4√2
We can calculate the distance between the points A'(4, -12) and B'(8, -16) in the same way:
d' = √((x₂ - x₁)² + (y₂ - y₁)²)
d' = √((8 - 4)² + (-16 - (-12))²)
d' = √((4)² + (-4)²)
d' = √(16 + 16)
d' = √32
d' = 4√2
Since the dilation is centered at the origin, the scale factor can be calculated as the ratio of the distances:
Scale factor = d' / d
Scale factor = (4√2) / (4√2)
Scale factor = 1
Therefore, the scale factor used in the dilation of line segment AB centered at the origin is 1.
The distance between the points A(4, -12) and B(8, -16) can be calculated as follows:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
d = √((8 - 4)² + (-16 - (-12))²)
d = √((4)² + (-4)²)
d = √(16 + 16)
d = √32
d = 4√2
We can calculate the distance between the points A'(4, -12) and B'(8, -16) in the same way:
d' = √((x₂ - x₁)² + (y₂ - y₁)²)
d' = √((8 - 4)² + (-16 - (-12))²)
d' = √((4)² + (-4)²)
d' = √(16 + 16)
d' = √32
d' = 4√2
Since the dilation is centered at the origin, the scale factor can be calculated as the ratio of the distances:
Scale factor = d' / d
Scale factor = (4√2) / (4√2)
Scale factor = 1
Therefore, the scale factor used in the dilation of line segment AB centered at the origin is 1.