Question

triangle rst is rotated 180 degrees clockwise around the origin, resulting in triangle rst. which statement is true?○ the coordinates of r are (8, 1)○ the coordinates of s are (3, 0)○ the coordinates of t are (3, -6)○ the coordinates of t are (6, 3)

Explanation:

Step1: Identify original coordinates

Original points: $R(-1, 8)$, $S(0, -3)$, $T(-5, -3)$

Step2: Apply 180° rotation rule

For a 180° clockwise rotation around the origin, the rule is $(x,y) \to (-x,-y)$.

• For $R(-1,8)$: $R'(1, -8)$
• For $S(0,-3)$: $S'(0, 3)$
• For $T(-5,-3)$: $T'(5, 3)$

Step3: Match with options

Compare calculated coordinates to given options.

Answer:

None of the provided options are correct based on the rotation rule. However, if there is a typo in the last option and it is meant to be $T'(5, 3)$, that would be the correct choice. Based on the exact options given, no option is mathematically accurate.

Note: Rechecking the rotation: A 180° rotation (clockwise or counterclockwise) around the origin inverts the sign of both x and y coordinates. The original $T$ is $(-5,-3)$, so rotated $T'$ is $(5,3)$, which does not match any provided option exactly. The closest is the last option with a possible typo (6 instead of 5).