IDNLearn.com makes it easy to find the right answers to your questions. Whether it's a simple query or a complex problem, our community has the answers you need.
Sagot :
To determine the image of the point [tex]\((1, -6)\)[/tex] after a [tex]\(90^{\circ}\)[/tex] counterclockwise rotation about the origin, we follow these steps:
1. Understand the transformation: A [tex]\(90^{\circ}\)[/tex] counterclockwise rotation about the origin in a Cartesian coordinate system transforms a point [tex]\((x, y)\)[/tex] to [tex]\((-y, x)\)[/tex].
2. Identify the original coordinates: The coordinates of the original point are [tex]\((1, -6)\)[/tex].
3. Apply the transformation:
- The [tex]\(x\)[/tex]-coordinate of the new point will be the negative of the original [tex]\(y\)[/tex]-coordinate. Thus, the new [tex]\(x\)[/tex]-coordinate is [tex]\(-(-6) = 6\)[/tex].
- The [tex]\(y\)[/tex]-coordinate of the new point will be the original [tex]\(x\)[/tex]-coordinate. Thus, the new [tex]\(y\)[/tex]-coordinate is [tex]\(1\)[/tex].
4. Resulting coordinates: After applying the transformation, the new coordinates are [tex]\((6, 1)\)[/tex].
Therefore, the image of the point [tex]\((1, -6)\)[/tex] after a [tex]\(90^{\circ}\)[/tex] counterclockwise rotation about the origin is [tex]\((6, 1)\)[/tex].
1. Understand the transformation: A [tex]\(90^{\circ}\)[/tex] counterclockwise rotation about the origin in a Cartesian coordinate system transforms a point [tex]\((x, y)\)[/tex] to [tex]\((-y, x)\)[/tex].
2. Identify the original coordinates: The coordinates of the original point are [tex]\((1, -6)\)[/tex].
3. Apply the transformation:
- The [tex]\(x\)[/tex]-coordinate of the new point will be the negative of the original [tex]\(y\)[/tex]-coordinate. Thus, the new [tex]\(x\)[/tex]-coordinate is [tex]\(-(-6) = 6\)[/tex].
- The [tex]\(y\)[/tex]-coordinate of the new point will be the original [tex]\(x\)[/tex]-coordinate. Thus, the new [tex]\(y\)[/tex]-coordinate is [tex]\(1\)[/tex].
4. Resulting coordinates: After applying the transformation, the new coordinates are [tex]\((6, 1)\)[/tex].
Therefore, the image of the point [tex]\((1, -6)\)[/tex] after a [tex]\(90^{\circ}\)[/tex] counterclockwise rotation about the origin is [tex]\((6, 1)\)[/tex].
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.