Question

A triangle has vertices at F (8, 3), G (3, 5), and H (1, 7). What are the coordinates of each vertex if the triangle is rotated 180° about the origin counterclockwise?

Question 1 options:

F ¢(8, 3), G¢(-3, 5), H ¢(-1, -7)


F ¢(8, -3), G ¢(3, -5), H ¢(1, -7)


F ¢(-8, 3), G¢(-3, 5), H ¢(-1, 7)


F ¢(-8, -3), G ¢(-3, -5), H ¢(-1, -7)

Answer 1

Answer: F (-8, -3), G (-3, -5) and H (-1, -7)

Explanation:

A rotation of 180° around the origin is equivalent to a reflection over the x-axis, and then another reflection over the y-axis.

Then, if we have a point (x, y) and we do a rotation of 180°, the point will transform into (-x, -y)

Then if at the start the vertices of the triangle are:

F (8, 3), G (3, 5), and H (1, 7).

After a rotation of 180°, the vertices will be:

F (-8, -3), G (-3, -5) and H (-1, -7)

The correct option is the last one.