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)

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)

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.

step-by-step explanation:

through just a quick inspection, one can see that the graph of this cubing function starts in quadrant iii and ends in quadrant i.   when x = 0, y = 3, so the y-intercept is (0, 3).

if graphs are part of the problem statement, share them.   .