Question

Which of the following represents a rotation of △LMN, which has vertices L(4,5), M(0,2), and N(−2,−4), about the origin by 180°?

Answers
a)
L (−4, −5)
M (2, 4)
N (0, −2)

b)
L (−5, −4)
M (−2, 0)
N (4, 2)

c)
L (−4, −5)
M (0, −2)
N (2, 4)

Answer 1

L (−4, −5)

M (0, −2)

N (2, 4)

Explanation:

The rule for this particular rotation is: (x, y)→(−x, −y).

To visualize why this is the case, the rotation can also be seen as the 180°clockwise rotation of the x- and y- axes about the origin while the figure remains in place. This rotation changes all x distances into x distances of the opposite sign, and all y distances into y distances of the opposite sign.

Apply the rule to each of the vertices of the triangle.

L(4, 5) → L'(−4, −5)

M (0, 2) → M' (0, −2)

N (−2, −4) → N' (2, 4)

Therefore, the coordinates of the vertices of the rotated triangle are

L' (−4, −5)

M' (0, −2)

N' (2, 4)

Answer 2

C

Explanation:

Geometrically: if we set a circle at the point of origin and it's radius is one of the points (I used L), then we simple rotate the point 180 degrees around the circle and discover our new coordinate.

doing this for all three points yields C.