Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To find the location of [tex]\( X^ \)[/tex] starting with the point [tex]\( X \)[/tex] at coordinates [tex]\((8, 4)\)[/tex], we need to follow two transformations: a translation and a reflection. Here are the steps:
1. Translation: The translation rule given is [tex]\((x, y) \rightarrow (x + 4, y - 1)\)[/tex].
- For the point [tex]\( X \)[/tex] at coordinates [tex]\((8, 4)\)[/tex]:
- The new [tex]\( x \)[/tex]-coordinate after translation: [tex]\( 8 + 4 = 12 \)[/tex].
- The new [tex]\( y \)[/tex]-coordinate after translation: [tex]\( 4 - 1 = 3 \)[/tex].
- So, after translation, the coordinates are [tex]\((12, 3)\)[/tex].
2. Reflection across the [tex]\( y \)[/tex]-axis: Reflecting a point across the [tex]\( y \)[/tex]-axis changes the sign of the [tex]\( x \)[/tex]-coordinate while keeping the [tex]\( y \)[/tex]-coordinate the same.
- For the translated point at coordinates [tex]\((12, 3)\)[/tex]:
- The new [tex]\( x \)[/tex]-coordinate after reflection: [tex]\(-12\)[/tex].
- The [tex]\( y \)[/tex]-coordinate remains the same: [tex]\( 3 \)[/tex].
- So, after reflection, the coordinates are [tex]\((-12, 3)\)[/tex].
Hence, the location of [tex]\( X^ \)[/tex] after performing both transformations is [tex]\((-12, 3)\)[/tex].
1. Translation: The translation rule given is [tex]\((x, y) \rightarrow (x + 4, y - 1)\)[/tex].
- For the point [tex]\( X \)[/tex] at coordinates [tex]\((8, 4)\)[/tex]:
- The new [tex]\( x \)[/tex]-coordinate after translation: [tex]\( 8 + 4 = 12 \)[/tex].
- The new [tex]\( y \)[/tex]-coordinate after translation: [tex]\( 4 - 1 = 3 \)[/tex].
- So, after translation, the coordinates are [tex]\((12, 3)\)[/tex].
2. Reflection across the [tex]\( y \)[/tex]-axis: Reflecting a point across the [tex]\( y \)[/tex]-axis changes the sign of the [tex]\( x \)[/tex]-coordinate while keeping the [tex]\( y \)[/tex]-coordinate the same.
- For the translated point at coordinates [tex]\((12, 3)\)[/tex]:
- The new [tex]\( x \)[/tex]-coordinate after reflection: [tex]\(-12\)[/tex].
- The [tex]\( y \)[/tex]-coordinate remains the same: [tex]\( 3 \)[/tex].
- So, after reflection, the coordinates are [tex]\((-12, 3)\)[/tex].
Hence, the location of [tex]\( X^ \)[/tex] after performing both transformations is [tex]\((-12, 3)\)[/tex].
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.