Question

Which statement explains the relationship of sides BA and B'A' after rectangle BADC has been rotated 90° clockwise about the origin?
coordinate plane with rectangle ABCD at A 3 comma 5, B 1 comma 3, C 5 comma negative 1, and D 7 comma 1

Side B'A' has a slope of −1 and is perpendicular to side BA.
Side B'A' has a slope of 1 and is parallel to side BA.
Side B'A' has a slope of 1 and is perpendicular to side BA.
Side B'A' has a slope of −1 and is parallel to side BA.

Answer 1

For this question malabrec31 is correct. Although, I saw confusion in the comments.

This question may be slightly different for other people.

If we took this question but had counterclockwise instead of clockwise, the answer would be altered. We would move from (x,y) to (-x,y).

I have attached the graph.

We can see the slope of BA is 1, this is 2/2 following rise/run. If we then rotate the figure 90 degrees counterclockwise segment B'A' would have a slope of 2/-2, this is the same as -1.

Now we can take out answer choices B and C.

Next, we need to figure out if the new segment is parallel or perpendicular to the original segment.

If you imagine what the two figures look like in the graph attached, you can see they would not be parallel.

If we rotated counterclockwise instead of clockwise the answer would be A, "Side B'A' has a slope of -1 and is perpendicular to side BA."

This is not the answer to the given question but instead to clarify for the viewers. Thank you.

Answer 2

Answer:

Side B'A has a slope of 1 and is perpendicular to side BA

Step-by-step explanation:

When rotating clockwise 90 degrees x,y will become y,-x so lets apply this to the points.

A=(3,5) -->(5,-3)

B=(1,3)-->(3,-1)

C=(5,-1)-->(-1,-5)

D=(7,1)-->(1,-7)

Now that we have the coordinates for A'B'C'D' we will graph both rectangles, (you can do this using Geogebra you wont need an account)once graphed we can draw a long straight line using a straightedge through points BA and B'A' to see that they eventually intersect and the line through B'A' goes through 1 on the x-axis.