Question

After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are A'(5, 3), B'(–2, 1), and C'(1, 7). What are the coordinates of the vertices of the pre-image?

A –

B –

C –

1. linhdan
The coordinates of the vertices of the preimages are A ( 3, 5) , B ( 1, 2) and C ( 7, -1)

### How to determine the coordinates

It is important to note the following about the 90 degrees rotation about the origin
• A( x ,y ) becomes A’ ( -y,  x )
• switch x and y and make y negative
Note that
A ( x, y) is the coordinates of the preimage
A’ ( -y , x) is the coordinates after the said rotation about the origin
Converting the transformed coordinates to the preimage coordinates
For vertex A
A’ ( 5, 3)
Compare with A’ ( -y, x)
x = 3
y = -5
Substitute the values
A ( 3, 5 )
For vertex B
B’ ( -2, 1)
Compare with B’ ( -y, x)
x = 1
y = 2
Substitute the values
B ( 1, 2)
For vertex C
C’ ( 1, 7)
Compare with C’ ( -y, x)
x = 7
y = -1
Substitute the values
C ( 7, -1)
Thus, the coordinates of the vertices of the preimages are A ( 3, 5) , B ( 1, 2) and C ( 7, -1)