Difference between revisions of "2022 AMC 12B Problems/Problem 5"

Revision as of 19:57, 17 November 2022

Problem

The point $(-1, -2)$ is rotated $270^{\circ}$ counterclockwise about the point $(3, 1)$ . What are the coordinates of its new position?

$\textbf{(A)}\ (-3, -4) \qquad \textbf{(B)}\ (0,5) \qquad \textbf{(C)}\ (2,-1) \qquad \textbf{(D)}\ (4,3) \qquad \textbf{(E)}\ (6,-3)$

Solution 1

$(-1,-2)$ is 4 units west and 3 units south of $(3,1)$ . Performing a counterclockwise rotation of $270^{\circ}$ , which is equivalent to a clockwise rotation of $90^{\circ}$ , the answer is 3 units west and 4 units north of $(3,1)$ , or $\boxed{\textbf{(B)}\ (0,5)}$ .

~ Bxiao31415

2022 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

@@ Line 5: / Line 5: @@
 == Solution 1 ==
-<math>(-1,-2)</math> is 4 units west and 3 units south of <math>(3,1)</math>. After a counterclockwise rotation of <math>270^{\circ}</math>, which is a clockwise rotation of <math>90^{\circ}</math>, it will end up 3 units west and 4 units north of <math>(3,1)</math>, which is at <math>\fbox{(0,5) B}</math>.
+<math>(-1,-2)</math> is 4 units west and 3 units south of <math>(3,1)</math>. Performing a counterclockwise rotation of <math>270^{\circ}</math>, which is equivalent to a clockwise rotation of <math>90^{\circ}</math>, the answer is 3 units west and 4 units north of <math>(3,1)</math>, or <math>\boxed{\textbf{(B)}\ (0,5)}</math>.
 ~[[User: Bxiao31415 | Bxiao31415]]

Page

Toolbox

Search

Difference between revisions of "2022 AMC 12B Problems/Problem 5"

Revision as of 19:57, 17 November 2022

Problem

Solution 1

See also