Question

Pentagon ABCDE is shown on the coordinate plane below.

Answer 1

Point D will pass from (1,-2) to (-1,2)

The second choice is the correct one.

Answer 2

Answer:

Option 2 is correct. The ordered pair of D'(-1,2)

Step-by-step explanation:

If pentagon ABCDE is rotated 180° around origin to create pentagon A'B'C'D'E'

We need to find the ordered pair of point D'

We will use the formula of rotation of coordinate about origin.

$x'=x\cos\theta+y\sin\theta$

$y'=-x\sin\theta+y\cos\theta$

We need to find the coordinate of D' which is corresponding of D.

Coordinate of D: (1,-2)

$\text{Where, }x=1, y=-2\text{ and }\theta=180^{\circ}$

Now we find D':(x',y')

$x'=1\times \cos 180^{\circ}-2\times \sin 180^{\circ}=-1$

$y'=-1\times \sin 180^{\circ}-2\times \cos 180^{\circ}=2$

D' (-1,2)

Thus, The ordered pair of D'(-1,2)