the diagram shows a dilation of line ab about the origin o. determine the scale factor of the dilation by following these steps:
1. measure these lengths:
oa = units
oa = units

Question

the diagram shows a dilation of line ab about the origin o. determine the scale factor of the dilation by following these steps:
1. measure these lengths:
oa =   units
oa =   units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Coordinate Geometry", "Distance Formula" ], "new_concepts": [ "Dilation Scale Factor", "Dilation in Coordinate Plane" ], "current_concepts": [ "Coordinate Geometry", "Distance Formula", "Dilation Scale Factor", "Dilation in Coordinate Plane" ] } ## Identify coordinates of points O, A, and A' $$ \begin{aligned} O &= (0, 0) \ A &= (2, -1) \ A' &= (3, -1.5) \end{aligned} $$ ## Calculate the length of OA $$ \begin{aligned} OA &= \sqrt{(2 - 0)^2 + (-1 - 0)^2} \ &= \sqrt{4 + 1} \ &= \sqrt{5} \approx 2.24 \end{aligned} $$ ## Calculate the length of OA' $$ \begin{aligned} OA' &= \sqrt{(3 - 0)^2 + (-1.5 - 0)^2} \ &= \sqrt{9 + 2.25} \ &= \sqrt{11.25} \approx 3.35 \end{aligned} $$ 1. Measure these lengths: $OA =$ $\sqrt{5}$ units $OA' =$ $1.5\sqrt{5}$ units { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Dilation Scale Factor" ] }

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Question

Explanation:

Identify coordinates of points O, A, and A'

Calculate the length of OA

Calculate the length of OA'

Answer: