Question

What are the resulting vertices of triangle E'F'G' after rotating triangle EFG 180° about the origin

Answer 1

To rotate a shape 180º about the origin you have to switch the coordinates and invert their signs following the rule:

`(x,y)\to(-y,-x)`

First, you have to determine the coordinates of each vertex od ΔEFG

E(-3,-1)

F(2,1)

G(1,-4)

Next, apply the rule to the coordinates of each vertex to rotate the triangle:

`E(-3,-1)\to E^(\prime)\lbrack-(-1),-(-3)\rbrack=E^(\prime)(1,3)`
`F(2,1)\to F^(\prime)(-1,-2)`
`G(1,-4)\to G^(\prime)\lbrack-(-4),-1\rbrack=G^(\prime)(4,-1)`

So, the coordinates of ΔE'F'G' are

E'(1,3)

F'(-1,-2)

G'(4,-1)