（1）the anwser of number 1 can be any point ,because you didnt tell me rotate around which point
(rotate around point A ,C'(-1,-3)
rotate around Point B C'(-3,1）
rotate around point C , the martix of point Cno change (2,2)
rotate around the origin , C'(-2,-2)
In numbe 2 , I guess the image rotate around point (-1,1) clockwise 90 degrees , so the marix of point B' is (2,1)
(3)the figure rotate around point H（-2,2）counterclockwise 90 degrees,then the marix of point E is (-2,7)
(4) the figure rotate around point C (2,2) clockwise 90 degrees ,then the martix of point B' is (0,-1)
in the isosceles triangle ABC, segment AD is the height of triangle from point A,and segment BE is the height of the triangle from point Learn from point B.
because triangle ABC is a isosceles triangle ,so AB=AC ,and segment AD is the height of the triangle
so angle ADB= Angle ADC=90 degrees
In the right triangle ADB and right triangle ADC
AB=AC,AD=AD, so right triangle ADB is congruent to right triangle ADC ( hypotenuse-leg)
so angle BAD= Angle CAD
If angle BAD=x degrees ,then angle BAC= 2x degrees
AD=AB*cosx DB=AB*sinx BE=AB*sin2x
the area of triangle = BD *AD*2/2=BD*AD=BE*AC/2=BE*AB/2
AB*cosx *AB*sinx=AB*sin2x*AB/2 (cancel AB*AB from both side and both side times 2)
this is my method,Can someone prove it algebraicallly?
okay the original question is In a trilsupose a lawyerwants 2 men and 5 womento make up a special panel.if the 7 panel menbers are selected at random fro a pool of 12 peoples,which istheprobality that the lawyer will not get the desired panel?(sorry for i didnt write the question completelyand i got the anwser）
ok i got it know.Thank you for your help.
why 0!=1? can n be a negative or fraction in n! ?why or why not?
This is a kind of ACt pratice problem in Mississippi ACT Exam Prep workbook. Accctually, the triangle ABC has a height of 1.5 units.But i think it can not be,becasue the height of the triangle ABC should be shorter than the radius.And the area of the triangle ABC is 2.25 units square.So the base of the triangle ABC is 3 units.I am wondering how they get 3.I put the problem into the forum because i think they did wrong on this problem. And i want to find ot the anwser togerther.