Question

Triangle PQR is rotated 180 degrees clockwise about the origin to produce the image Triangle P’Q’R’. Which of the following statements is TRUE abóyate Triangle P’Q’R’.

Answer 1

Triangle PQR rotated 180 degrees clockwise about the origin results in Triangle P'Q'R', which preserves the distances between points and from points to the origin due to the isometric nature of the rotation.

Step-by-step explanation:

When Triangle PQR is rotated 180 degrees clockwise about the origin, the resulting Triangle P'Q'R' will have vertices that are the reflections of the original vertices about the origin. The relationship between the coordinates of the original points and the coordinates of the rotated points can be described as follows for a 180-degree rotation:

For any point (x, y), after a 180-degree rotation, the new coordinates will be (-x, -y).

This transformation does not change the distance between any two points, or between a point and the origin, because a rotation is an isometric transformation (i.e., it preserves distances). Thus, the following statements can be made:

The distance between points P and Q is invariant under a 180-degree rotation.

The distance of point P to the origin is also invariant under a 180-degree rotation.

The precise mathematical expressions for these invariants are not necessary for this explanation, as the concept of distance preservation under rotation is a fundamental property of isometric transformations.

Answer 2

Step-by-step explanation:

We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is: P (1, 4) → P' (-1, -4) Q (3, 1) → Q' (-3, -1) R (2, -1) → R' (-2, 1) Thus, the new position of ∆PQR is ∆P’Q’R’.