Question

the coordinates of a quadrilateral are (5,8), (7,10), (9,12) and (11,14). after a transformation, the sign of the x-coordinate and the sign of the y- coordinate for each ordered pair have changed. which type of transformation occurred?

Answer 1

Answer:

The quadrilateral is rotated 180° about the origin

Step-by-step explanation:

Lets revise some transformation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

∴ Its image is (-y , -x)

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise or

 anti-clockwise around the origin

* In our problem:

- The sign of the x-coordinate and the sign of the y- coordinate

 for each ordered pair have changed

- The image of each point is (-5 , -8) , (-7 , -10) , (-9 , -12) , (-11 , -14)

∴ The quadrilateral is rotated 180° about the origin