|
|
| Line 2: |
Line 2: |
| size(288); | | size(288); |
|
| |
|
| pair A, B, C, D;
| | draw((-3,0)--(3,0)); dot((0,0)); label("$O$",(0,0),N); |
| A = (0,0); B = (5,0); C = (7,4); D = (2,4);
| | draw((0,0)--(2,0),Arrow); dot((1,0),blue); dot((-2,0),darkgreen); |
| draw((-1,0)--(8,0)); draw((-1,4)--(8,4)); draw((-1,-2)--(3,6)); draw((4,-2)--(8,6)); | | label("$P$",(1,0),N); label("$Q$",(-2,0),N); |
| draw((-1,-4/7)--(8,32/7)); draw((13/2,-2)--(1/2,6));
| |
| | |
| dot(A); dot(B); dot(C); dot(D);
| |
| label("$A$",A,NW); label("$B$",B+(0,-1/5),S); label("$C$",C,SE); label("$D$",D+(0,1/5),N);
| |
| | |
| label("$64^\circ$",D+(1/10,-1/2),S); label("$34^\circ$",(-7/10,-11/14));
| |
| label("$x$",(5/2,15/4)); label("$y$",(25/4,15/4)); label("$z$",(3,2));
| |
| </asy>
| |
| | |
| <asy>
| |
| size(288);
| |
| | |
| real e = 2.718281828459045235360287471352662497757247093699959574966967627724076630353;
| |
| real pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286;
| |
| | |
| xaxis(-3,11);
| |
| yaxis(-2,12);
| |
| | |
| real f(real x) { return (x/2 + 1) * (x/2 - 2) * (x/2 - 3); }
| |
| | |
| draw(graph(f,-3,11)); draw((0,6)--(8,10));
| |
| | |
| dot((0,6)); dot((8,10)); dot((-2,0)); dot((4,0)); dot((6,0)); | |
| label("$A$",(0,6),NW); label("$B$",(8,10),E); label("$(-1,0)$",(-2,0),SE); label("$(2,0)$",(4,0),SW); label("$(3,0)$",(6,0),SE); | |
| | |
| limits((-3,-3),(11,12),Crop);
| |
| </asy>
| |
| | |
| <asy>
| |
| import three; import graph3;
| |
| currentprojection=orthographic(4,-4,1);
| |
| size(288);
| |
| | |
| //xaxis3("$A$",0,3);
| |
| //yaxis3("$A'$",0,3);
| |
| zaxis3("$\hat{\mathbf{n}}$",0,1);
| |
| | |
| draw((3,0,0)--(0,4,0)--(-3,0,0)--(0,-4,0)--cycle); draw((1,0,1)--(0,0,0)--(1,0,-1)); draw((0,0,0)--(1,0,0)); draw((1,0,1)--(1,0,-1),dashed); | |
| | |
| label("$\mathbf{x}$",(1,0,1),E); label("$\mathbf{x}'$",(1,0,-1),E); | |
| </asy> | | </asy> |
![[asy] size(288); draw((-3,0)--(3,0)); dot((0,0)); label("$O$",(0,0),N); draw((0,0)--(2,0),Arrow); dot((1,0),blue); dot((-2,0),darkgreen); label("$P$",(1,0),N); label("$Q$",(-2,0),N); [/asy]](http://latex.artofproblemsolving.com/5/f/6/5f6fe95096587c6c66d04e39990bf78bb560a904.png)
