Difference between revisions of "2020 AMC 12A Problems/Problem 6"
(Created page with "Line <math>\ell</math> in the coordinate plane has the equation <math>3x - 5y + 40 = 0</math>. This line is rotated <math>45^{\circ}</math> counterclockwise about the point <m...") |
|||
| Line 1: | Line 1: | ||
| − | + | ==Problem 6== | |
| − | <math>\textbf{(A) } | + | In the plane figure shown below, <math>3</math> of the unit squares have been shaded. What is the least number of additional unit squares that must be shaded so that the resulting figure has two lines of symmetry? |
| + | |||
| + | <asy> | ||
| + | import olympiad; | ||
| + | unitsize(25); | ||
| + | filldraw((1,3)--(1,4)--(2,4)--(2,3)--cycle, gray(0.7)); | ||
| + | filldraw((2,1)--(2,2)--(3,2)--(3,1)--cycle, gray(0.7)); | ||
| + | filldraw((4,0)--(5,0)--(5,1)--(4,1)--cycle, gray(0.7)); | ||
| + | for (int i = 0; i < 5; ++i) { | ||
| + | for (int j = 0; j < 6; ++j) { | ||
| + | pair A = (j,i); | ||
| + | |||
| + | } | ||
| + | } | ||
| + | for (int i = 0; i < 5; ++i) { | ||
| + | for (int j = 0; j < 6; ++j) { | ||
| + | if (j != 5) { | ||
| + | draw((j,i)--(j+1,i)); | ||
| + | } | ||
| + | if (i != 4) { | ||
| + | draw((j,i)--(j,i+1)); | ||
| + | } | ||
| + | } | ||
| + | } | ||
| + | </asy> | ||
| + | |||
| + | <math>\textbf{(A) } 4 \qquad \textbf{(B) } 5 \qquad \textbf{(C) } 6 \qquad \textbf{(D) } 7 \qquad \textbf{(E) } 8</math> | ||
Revision as of 15:49, 1 February 2020
Problem 6
In the plane figure shown below, 
of the unit squares have been shaded. What is the least number of additional unit squares that must be shaded so that the resulting figure has two lines of symmetry?
![[asy] import olympiad; unitsize(25); filldraw((1,3)--(1,4)--(2,4)--(2,3)--cycle, gray(0.7)); filldraw((2,1)--(2,2)--(3,2)--(3,1)--cycle, gray(0.7)); filldraw((4,0)--(5,0)--(5,1)--(4,1)--cycle, gray(0.7)); for (int i = 0; i < 5; ++i) { for (int j = 0; j < 6; ++j) { pair A = (j,i); } } for (int i = 0; i < 5; ++i) { for (int j = 0; j < 6; ++j) { if (j != 5) { draw((j,i)--(j+1,i)); } if (i != 4) { draw((j,i)--(j,i+1)); } } } [/asy]](http://latex.artofproblemsolving.com/0/9/8/098f8098c7103b004757d1977d2bd6d459831eb3.png)
