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)

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

investment b is an ordinary annuity with $3,909.64 in the account after one year.

step-by-step explanation: