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4 years ago

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Which statement explains the relationship of sides BA and B'A' after rectangle BADC has been rotated 90° clockwise about the ori

gin?
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.

1 answer:

Leni [432]4 years ago

8 0

Answer:

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;

$Slope \, of BA= \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}} =\dfrac{3-5}{1-3}= \dfrac{-2}{-2} = 1$

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;

$Slope \, of \, B'A' =\dfrac{-1 -(-3)}{3-5}= \dfrac{2}{-2} = -1$

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

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Hello there!

$14.8=n-0.3$

Answer:

$\boxed{n=15.1=15.0}$

You can also round up to the nearest tenths is 15.1 to 15.0 and its going to be stay.

Step-by-step explanation:

First you had to switch sides of equation form.

$n-0.3=14.8$

Then you add by 0.3 from both sides of equation form.

$n-0.3+0.3=14.8+0.3$

And finally, simplify by equation. You can also cross out by -0.3+0.3 and it gave us equal to zero. Then you add 14.8+0.3 and it equal to 15.1. You had to used their variable and its should be the right answer.

$n=15.1$

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$\mathrm{curl}\vec F=\dfrac{\partial(5x+10y)}{\partial x}-\dfrac{\partial(-6x+5y)}{\partial y}=5-5=0$

We want to find $f$ such that $\nabla f=\vec F$ . This means

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