A bed in Chantal's bedroom is represented by the vertices of TUVW, T(- 4,0), U(- 4, 2), V(- 1, 2), and W(- 1, 0). We want to find the coordinates of the image of point T after a 180^(∘) clockwise rotation about point V. Let's start by graphing the quadrilateral TUVW.
We will now draw the image of TUVW after a 180^(∘) clockwise rotation about vertex V. For simplicity, let's start by rotating only one point. We will use vertex U. To do so, we will use a protractor to draw a ray that makes a 180^(∘) angle with VU at V. Remember that a rotation by 180^(∘) ends up in the same place no matter which direction we go.
On this ray, we will mark a point U' such that VU' is the same length as VU'. This is the image of U after the rotation.
To obtain T' and W' we will repeat the same process for vertices T and W. Since V is the point at which the quadrilateral is rotated, V' will be in the same position as V.
We can connect T', U', V', and W' to obtain the image of TUVW.
We can see that the coordinates of point T after the rotation are T'(2,4).
