Question
The scale factor of G2H is one to seven. What is the measurement of x and y
X equals one and Y equals 14
X equals one and Y equals seven
X equals two and Y equals seven
X equals two and Y equals 14
X equals one and Y equals 14
X equals one and Y equals seven
X equals two and Y equals seven
X equals two and Y equals 14
Answers
Answered by
GPT-4o mini
To determine the correct values of \( x \) and \( y \) based on the given scale factor of 1 to 7 for G2H, we should understand that for any geometric shape, the scale factor represents the ratio of lengths between corresponding dimensions in the original shape (G) and the scaled shape (H).
Since the scale factor is 1 to 7, every original measurement would be multiplied by 7 to get the new measurement.
If we check the options provided:
1. \( x = 1 \) and \( y = 14 \): This works since \( 1 \times 7 = 7 \) (for one dimension) and \( 14 \div 7 = 2 \).
2. \( x = 1 \) and \( y = 7 \): This is also correct as \( 1 \times 7 = 7\) and \( 7 \div 7 = 1 \).
3. \( x = 2 \) and \( y = 7 \): This could also be correct; \( 2 \times 7 = 14\) and \( 7 \div 7 = 1 \).
4. \( x = 2 \) and \( y = 14 \): This works since \( 2 \times 7 = 14\) and \( 14 \div 7 = 2 \).
Each pair of values can correspond to the scale factor of 1 to 7, but they represent different scenarios of original dimensions versus scaled dimensions. In essence, you could choose any of these pairs depending on what quantities \( x \) and \( y \) are representing.
Based on the context given, if you wish to find the one that expresses 1 in the original and 7 in the scaled version directly, or the most likely scenario, the option "X equals one and Y equals seven" or "X equals two and Y equals fourteen" could signify the fundamental reference when analyzing similar triangles or shapes.
Hence, all the options could represent valid points depending on interpretations, but \( x = 1\) and \( y = 7\) fits standard geometric scaling best.
Since the scale factor is 1 to 7, every original measurement would be multiplied by 7 to get the new measurement.
If we check the options provided:
1. \( x = 1 \) and \( y = 14 \): This works since \( 1 \times 7 = 7 \) (for one dimension) and \( 14 \div 7 = 2 \).
2. \( x = 1 \) and \( y = 7 \): This is also correct as \( 1 \times 7 = 7\) and \( 7 \div 7 = 1 \).
3. \( x = 2 \) and \( y = 7 \): This could also be correct; \( 2 \times 7 = 14\) and \( 7 \div 7 = 1 \).
4. \( x = 2 \) and \( y = 14 \): This works since \( 2 \times 7 = 14\) and \( 14 \div 7 = 2 \).
Each pair of values can correspond to the scale factor of 1 to 7, but they represent different scenarios of original dimensions versus scaled dimensions. In essence, you could choose any of these pairs depending on what quantities \( x \) and \( y \) are representing.
Based on the context given, if you wish to find the one that expresses 1 in the original and 7 in the scaled version directly, or the most likely scenario, the option "X equals one and Y equals seven" or "X equals two and Y equals fourteen" could signify the fundamental reference when analyzing similar triangles or shapes.
Hence, all the options could represent valid points depending on interpretations, but \( x = 1\) and \( y = 7\) fits standard geometric scaling best.