# How do I answer this question?Use the coordinate rules to rotate triangle ABC 90 degrees counterclockwise around the origin. List the coordinates and draw the image of triangle A'B'C'....

How do I answer this question?

Use the coordinate rules to rotate triangle ABC 90 degrees counterclockwise around the origin. List the coordinates and draw the image of triangle A'B'C'. (a,b)translates to(______,_____)

A(-1,-2)translates to A'(____,____)

B(1,2) translates to B'(______,____)

C(3,-1) translates to C'(______,____)

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Let coordinate of A'(x',y') ,A(-1,-2)=A(x,y)

we know

x'=xcos(theta)-ysin(theta)

y'=xsin(theta)+y cos(theta)

Thus

x'=(-1)cos(90)-(-2)sin(90)

x'=2

y'=-1sin(90)=-1 ,

**A'(x',y')=A'(2,-1)**

B(x,y)=B(1,2)

B'(x',y')=?

x'=1 cos(90)-2sin(90)=-2

y'=1sin(90)+2cos(90)=1

**B'(x',y')=B'(-2,1)**

C(x,y)=C(3,-1)

C(x',y')=?

x'=3cos(90)-1sin(90)=-1

y'=3sin(90)+1cos(90)=3

**C(x',y')=C(-1,3)**

**A(-1,-2)translates to A'(2,-1)B(1,2) translates to B'(-2,1)C(3,-1) translates to C'(-1,3)**