consider the graphs of figures abcd and efgh.
is figure abcd similar to figure efgh? select the correct answer.

yes, because the figure is stretched by the same amount both vertically and horizontally.
yes, because the figure is stretched vertically but not horizontally.
no, because the figure is stretched vertically but not horizontally.
no, because the figure is stretched by the same amount both vertically and horizontally.

Question

consider the graphs of figures abcd and efgh.
is figure abcd similar to figure efgh? select the correct answer.

yes, because the figure is stretched by the same amount both vertically and horizontally.
yes, because the figure is stretched vertically but not horizontally.
no, because the figure is stretched vertically but not horizontally.
no, because the figure is stretched by the same amount both vertically and horizontally.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Similarity Transformations", "Geometric Dilations" ], "current_concepts": [ "Dilation of Polygons", "Similarity Transformations", "Geometric Dilations" ] } ## Identify coordinates of vertices $$ \begin{aligned} &\text{Figure } ABCD:\ &A(-1, 2), \quad B(2, 2.5), \quad C(2, 1), \quad D(-1, 1)\ &\text{Figure } EFGH:\ &E(-1, 3), \quad F(2, 4), \quad G(2, 2), \quad H(-1, 2) \end{aligned} $$ ## Calculate horizontal and vertical dimensions $$ \begin{aligned} &\text{Width of } ABCD = x_C - x_D = 2 - (-1) = 3\ &\text{Width of } EFGH = x_G - x_H = 2 - (-1) = 3\ &\text{Horizontal Scale Factor } (k_x) = \frac{3}{3} = 1\ &\text{Height of } ABCD = y_A - y_D = 2 - 1 = 1\ &\text{Height of } EFGH = y_E - y_H = 3 - 2 = 1\ &\text{Height at right side of } ABCD = y_B - y_C = 2.5 - 1 = 1.5\ &\text{Height at right side of } EFGH = y_F - y_G = 4 - 2 = 2 \end{aligned} $$ ## Determine similarity $$ \begin{aligned} &\text{Vertical stretch factor on left side: } \frac{y_E - y_H}{y_A - y_D} = \frac{1}{1} = 1\ &\text{Vertical stretch factor on right side: } \frac{y_F - y_G}{y_B - y_C} = \frac{2}{1.5} = \frac{4}{3} \approx 1.33\ &\text{Since the vertical stretch is not uniform and horizontal stretch is 1, the figures are not similar.}\ &\text{Specifically, the figure is stretched vertically but not horizontally.} \end{aligned} $$

Yes, because the figure is stretched by the same amount both vertically and horizontally.

Yes, because the figure is stretched vertically but not horizontally.

No, because the figure is stretched vertically but not horizontally.

No, because the figure is stretched by the same amount both vertically and horizontally.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Similarity Transformations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coordinates of vertices

Calculate horizontal and vertical dimensions

Determine similarity

Answer: