Question

TOP is rotated - 180° about the origin.Find out for the blue triangle

Answer 1

A graph of triangle TOP and its image after a rotation 180° about the origin is shown in the picture below.

In Euclidean Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure about the origin by 180° is given by this mathematical expression:

(x, y) → (-x, -y)

Point T (6, 0) → Point T' = (-6, 0)

Point O (-2, -5) → Point O' = (2, 5)

Point P (-2, 5) → Point P' = (2, -5)

In this context, we can logically deduce that the coordinates of the image (△T'O'P') are T' (-6, 0), O' (2, 5), and P' (2, -5).

Complete Question:

△TOP is rotated -180° about the origin. Draw the image of this rotation.

Answer 2

We have the following general rule for the rotation of 180 degrees about the origin:

`R_(180)(x,y)=(-x,-y)`

in this case, we have the following points:

`\begin{gathered} T=(6,0) \\ O=(-2,-5) \\ P=(-2,5) \end{gathered}`

therefore, their rotation of 180 degrees about the origin is:

`\begin{gathered} T^(\prime)=R_(180)(6,0)=(-6,0) \\ O^(\prime)=R_(180)(-2,-5)=(2,5) \\ P^(\prime)=R_(180)(-2,5)=(2,-5) \end{gathered}`