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 (3,5), B (1,3), C (5,-1), and D (7,1)

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.

Option (4) will be the correct option.

   Coordinates of the vertices of rectangle ABCD are,

Slope of a segment with endpoints and is given by the expression,

Slope 'm' =

Therefore, slope of segment BA (m₁) = = 1

If a point (h, k) is rotated 90° clockwise about the origin, rule to be followed,

(h, k) → (-k, h)

Following this rule,

B(1, 3) → B'(-3, 1)

A(3, 5)→ A'(-5, 3)                        

Slope of segment B'A' (m₂) =

Expression representing two segments with slopes and to be perpendicular,

Since, slopes of two segments BA and B'A' are (1) and (-1).

(1) × (-1) = -1

Therefore, both the segments BA and B'A' will be perpendicular.

    Option (4) will be the answer.

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Numbering the options, we have;

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

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

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

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

The correct option is;

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

Step-by-step explanation:

The given coordinates are;

A(3, 5) B(1, 3), C(5, -1) and D(7, 1)

The slope of BA is found as follows;

Rotation of a line through 90 degrees gives

(x, y) will be (y, -x)

Therefore, the coordinates of A' = (5, -3)

The coordinates of B' = (3, -1)

Then the slope is given as follows;

Therefore side B'A' has a slope of -1 and is perpendicular to side BA.

it would open into a square depending on the type of envelope i’m not sure about the second part

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step-by-step explanation: