How can I find coordinates of the vertices of the figure after the given transformation?

Question

Rotation 180 degrees about the origin

E(2,-2), J(1,2), R(3,3), S(5,2)

Answer 1

A rotation of 180 degrees is the same as moving a given point halfway around the origin. It will be the same distance from the origin, but on the other side of it. This rotation is also equivalent to reflecting a point over the x-axis and then the y-axis.

 

A reflection over the x-axis just means a point's x-coordinate stays the same while its y-coordinate switches signs (positive becomes negative, negative becomes positive). A reflection over the y-axis means a point's y-coordinate stays the same while its x-coordinate switches signs.

 

So, a rotation by 180 degrees just means you should switch the signs of each point's x-coordinate and y-coordinate:

 

E(2, -2) becomes E'(-2, 2)

J(1, 2) becomes J'(-1, -2)

R(3, 3) becomes R'(-3, -3)

S(5, 2) becomes S'(-5, -2)

 

Plot these points to make sure they've all moved by 180 degrees.