Question

line segment EF is shown on the coordinate grid:The line segment is rotated by 270 degrees counterclockwise about the origin to form E'F'. Which statemeny describes E'F'.A) E'F' is parallel to EF.B) E'F' is equal in length to EF.C) E'F' is half the length of EF.D) E'F' is twice the length of EF.

Answer 1

Option B is correct.

E'F' is equal in length to EF.

Step-by-step explanation

When a figure is rotated through any degree clockwise or counterclockwise, the length of the figure stays the same.

This proves option B right and it proves options C and D wrong.

But to prove option A wrong, we need to find the coordinates of E'F'.

When a rotation of 270° counterclockwise about the origin is done on some coordinate, A (x, y), it transforms this coordinates into A' (y, -x). That is, we switch y and x, then add negative sign to x.

To obtain the coordinates of E' and F', we need to obtain the coordinates of E and F first.

E (1, -4)

F (5, -4)

When they are transformed through rotation of 270° counterclockwise about the origin, the change is that

A (x, y) = A' (y, -x)

E (1, -4) = E' (-4, -1)

F (5, -4) = F' (-4, -5)

E' (-4, -1) and F' (-4, -5) when marked out and drawn on this graph gives a vertical line that lies on x = -4 and covers from y = -1 to y = -5.

This indicates that E'F' is vertical and not horizontal like EF and thus, E'F' is not parallel to EF, rather, E'F' is perpendicular to EF.

Hope this Helps!!!