Is ΔP'Q'R' a 180° rotation about the origin of ΔPQR? Use the drop-down menus to explain your answer.

Answer: No, it isn't.

Step-by-step explanation: This graph shows a Translation, meaning the figure moved. Yes, the rotation of the second figure is 180 degrees, but it was also Translated downwards 2 points down and one to the right.

Yes, ΔP'Q'R' a 180° rotation about the origin of ΔPQR.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Midpoint of PQ: ((2+4)/2, (3+4)/2) = (3, 3.5)

QR: ((4+4)/2, (4+3)/2) = (4, 3.5)

RP: ((4+2)/2, (3+3)/2) = (3, 3)

Translate each midpoint to the origin by subtracting the coordinates of the midpoint from each vertex:

P translated: (2-3, 3-3.5) = (-1, -0.5)

Q translated: (4-4, 4-3.5) = (0, 0.5)

R translated: (4-3, 3-3) = (1, 0)

Rotate each translated vertex by 180° about the origin:

P' rotated: (-(-1), -(-0.5)) = (1, 0.5)

Q' rotated: (-0, -0.5) = (0, -0.5)

R' rotated: (-1, -0) = (1, 0)

Translate each rotated vertex back to its original position by adding the coordinates of the midpoint:

P' translated back: (1+3, 0.5+3.5) = (4, 4)

Q' translated back: (0+4, -0.5+3.5) = (4, 3)

R' translated back: (1+3, 0+3) = (4, 3)

We can see that the coordinates of P', Q', and R' match the coordinates of Q, R, and P respectively

ΔP'Q'R' is a 180° rotation about the origin of ΔPQR.

Hence, yes ΔP'Q'R' a 180° rotation about the origin of ΔPQR.

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