Given the vertices of ∆abc are a (2,-5), b (-4,6) and c (3,1), find the vertices following each of the transformations from the original vertices: a. rx = 3 b. t< 3,-6> c. r(90◦, o)

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)

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)

where are the choices?