Answers
a) R x=3: A¹(4,-5)
B¹(10, 6) and
C(3, 1)
b) T(3,-6): A¹(5, -1),
B¹(-1, 0) and
C¹(6, -5)
c) r(90⁰, 0): A¹(5, 2),
B¹(-6, -4) and
C¹(-1, 3)
Step-by-step explanation
R x=3:
The value of y wont change for reflection along line x=3.
The distance from 3 to 2 is 1 to the left, its image should be 1 units to the right. And so it is to the other points.
3+1 = 4. A¹(4, -5)
4+3=7.
3+7=10. B¹(10,6)
Point C is on the reflection line. its point wont change. C¹(3,1)
b) T(3,-6)
Translation you just add the vector of translation to get the image.
A¹(2,5) +(3,-6) = A¹(5, -1)
B¹(-4, 6)+(3, -6) = B¹(-1, 0)
C¹(3,1)+(3, -6) = C¹(6, -5)
c) r(90⁰, 0)
This is rotation of positive 90⁰ about the origin.
For rotation of positive 90⁰ about the origin, the points of the axis just interchange and the x coordinate changes the sign.
A(2, -5) ⇒ A¹(5, 2)
B(-4, 6) ⇒B¹(-6, -4)
C(3,1) ⇒ C¹(-1, 3)