Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

What are the new coordinates of point A when it is rotated about the origin by

a) [tex]90^{\circ}[/tex] clockwise?
b) [tex]180^{\circ}[/tex]?
c) [tex]270^{\circ}[/tex] clockwise?

Sagot :

GinnyAnswer
Sure! Let's walk through the transformations step by step for the given point [tex]\( A(1, 1) \)[/tex].

### a) Rotation by [tex]\(90^\circ\)[/tex] clockwise:
For a point [tex]\((x, y)\)[/tex], the transformation formulas for a [tex]\(90^\circ\)[/tex] clockwise rotation are:
- [tex]\( x' = y \)[/tex]
- [tex]\( y' = -x \)[/tex]

Applying these formulas to the point [tex]\( A(1, 1) \)[/tex]:
- [tex]\( x' = 1 \)[/tex]
- [tex]\( y' = -1 \)[/tex]

Thus, the new coordinates after a [tex]\(90^\circ\)[/tex] clockwise rotation are [tex]\((1, -1)\)[/tex].

### b) Rotation by [tex]\(180^\circ\)[/tex]:
For a point [tex]\((x, y)\)[/tex], the transformation formulas for a [tex]\(180^\circ\)[/tex] rotation are:
- [tex]\( x' = -x \)[/tex]
- [tex]\( y' = -y \)[/tex]

Applying these formulas to the point [tex]\( A(1, 1) \)[/tex]:
- [tex]\( x' = -1 \)[/tex]
- [tex]\( y' = -1 \)[/tex]

Thus, the new coordinates after a [tex]\(180^\circ\)[/tex] rotation are [tex]\((-1, -1)\)[/tex].

### c) Rotation by [tex]\(270^\circ\)[/tex] clockwise:
For a point [tex]\((x, y)\)[/tex], the transformation formulas for a [tex]\(270^\circ\)[/tex] clockwise rotation are:
- [tex]\( x' = -y \)[/tex]
- [tex]\( y' = x \)[/tex]

Applying these formulas to the point [tex]\( A(1, 1) \)[/tex]:
- [tex]\( x' = -1 \)[/tex]
- [tex]\( y' = 1 \)[/tex]

Thus, the new coordinates after a [tex]\(270^\circ\)[/tex] clockwise rotation are [tex]\((-1, 1)\)[/tex].

In summary:
a) After a [tex]\(90^\circ\)[/tex] clockwise rotation, the coordinates are [tex]\((1, -1)\)[/tex].
b) After a [tex]\(180^\circ\)[/tex] rotation, the coordinates are [tex]\((-1, -1)\)[/tex].
c) After a [tex]\(270^\circ\)[/tex] clockwise rotation, the coordinates are [tex]\((-1, 1)\)[/tex].
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.