Question

Parallelogram ABCD is reflected over the y-axis, followed by a reflection over the x-axis, and then rotated 180 degrees about the origin. What is the location of point A after the transformations are complete?
(−5, −1)

(5, 1)

(−5, 1)

(5, −1)

Answer 1

(-5,1) Because the two reflections make the figure go to the third quadrant. If you have a 180 degree rotation it’ll go back to the second quadrant

Answer 2

Answer: Third option. (-5, 1)

Solution:

Coordinates of the point A=(-5, 1)

1) Reflection over the y-axis

When you reflect a point P=(x,y) over the y-axis its coordinates changes to the point P'=(-x,y). In this case:

A=(-5, 1)=(xa, ya); xa=-5, ya=1→A'=(-xa, ya)=(-(-5), 1)→A'=(5, 1)

2) Reflection over the x-axis

When you reflect a point P=(x,y) over the x-axis its coordinates changes to the point P'=(x,-y). In this case:

A'=(5, 1)=(xa', ya'); xa'=5, ya'=1→A''=(xa', -ya')→A''=(5, -1)

3) Rotation 180° about the origin

When you ratate a point P=(x,y) 180° about the origin its coordinates changes to the point P'=(-x, -y). In this case:

A''=(5, -1)=(xa'', ya''); xa''=5, ya''=-1→A'''=(-xa'', -ya'')=(-5, -(-1))→A'''=(-5, 1)