Pregunta
Given \( \triangle A B C \) with vertices at \( -A(-4,-3), B(4,5) \), and \( C(5,-2) \), and if the triangle is dilated with a scale factor of 3 , find the coordinates of - \( C \). Select one: a. \( (5,-1) \) b. \( (15,-6) \) c. \( (3,-3) \) d. \( (2,4) \)
Ask by Kirk Wright. in the United States
Mar 13,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The coordinates of the dilated point \( C \) are \( (15, -6) \).
Solución
1. The dilation transformation with a scale factor of 3 multiplies each coordinate of a point by 3. That is, a point \((x, y)\) becomes \((3x, 3y)\).
2. For point \( C(5,-2) \):
\[
x' = 3 \times 5 = 15, \quad y' = 3 \times (-2) = -6.
\]
3. Therefore, the coordinates of the dilated \( C \) are \((15,-6)\).
The correct answer is \( (15,-6) \).
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Simplifique esta solución Beyond the Answer
To find the coordinates of point \( C \) after dilation with a scale factor of 3, we first determine the coordinates of \( C \), which are \( (5, -2) \). Using the formula for dilation, which is given by \( (x, y) \) becoming \( (kx, ky) \), where \( k \) is the scale factor, we calculate the new coordinates of \( C \): - New \( x \) coordinate: \( 3 \times 5 = 15 \) - New \( y \) coordinate: \( 3 \times (-2) = -6 \) So, the dilated coordinates of \( C \) are \( (15, -6) \). The correct answer is: b. \( (15,-6) \)
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