Question

(04.02 HC) Which statement explains the relationship of sides BA and B'A' after rectangle BADC has been rotated 180° 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

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

Answer 2

The slope of BA and slope of B'A' are the same that is 1. So, the correct option is B). Side B'A' has a slope of 1 and is parallel to side BA and this can be determined by finding the slope of sides BA and B'A'.

Given :

• Rectangle BADC.

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

Evaluate the slope of BA and B'A' in order to determine which statement is correct.

The slope of BA is given by:

$\rm m_1 = \dfrac{y_2-y_1}{x_2-x_1}$

Now, put the values of $(x_1,y_1)$ and $(x_2,y_2)$ in the above equation.

$\rm m_1 = \dfrac{5-3}{3-1}$

$\rm m_1 = 1$

After the rotation of $180^\circ$ point (x,y) becomes (-x,-y). So, point A(3,5) becomes A'(-3,-5) and point B(1,3) becomes B'(-1,-3).

The slope of B'A' is given by:

$\rm m_2 = \dfrac{y_2-y_1}{x_2-x_1}$

Now, put the values of $(x_1,y_1)$ and $(x_2,y_2)$ in the above equation.

$\rm m_2 = \dfrac{-5+3}{-3+1}$

$\rm m_2 = 1$

Therefore, the slope of BA and slope of B'A' are the same that is 1. So, the correct option is B). Side B'A' has a slope of 1 and is parallel to side BA.

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https://brainly.com/question/18666670