Pregunta
In \( \triangle F G H \), the coordinates of vertex \( H \) are \( (x, y) \) What are the coordinates of vertex \( H^{\prime} \) under a dilation centered at the origin with scale factor \( \frac{5}{3} \) ?
Ask by Pearson Wagner. in the United States
Mar 12,2025
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The coordinates of vertex \( H^{\prime} \) are \( \left(\frac{5}{3}x, \frac{5}{3}y\right) \).
Solución
1. A dilation centered at the origin with a scale factor of \( \frac{5}{3} \) transforms any point \( (x, y) \) to the point
\[
\left(\frac{5}{3}x, \frac{5}{3}y\right).
\]
2. Therefore, the coordinates of vertex \( H^{\prime} \) are
\[
\left(\frac{5}{3}x, \frac{5}{3}y\right).
\]
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Under a dilation centered at the origin with a scale factor of \( \frac{5}{3} \), the coordinates of any point \((x, y)\) are multiplied by the scale factor. Therefore, the coordinates of vertex \( H^{\prime} \) will be: \[ H^{\prime} = \left( \frac{5}{3}x, \frac{5}{3}y \right) \] This means that both the x-coordinate and y-coordinate of vertex \( H \) are scaled by \( \frac{5}{3} \). So if you plug in the values of \( x \) and \( y \), you'll get the new coordinates of \( H^{\prime} \).
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