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3 years ago

Which box shows a reflection across both axes?

Mathematics

1 answer:

Liula [17]3 years ago

8 0

We want: P(x,y) => P'(-x,-y)

Check each one:

A)
P(5,5) => P'(5,-5) Wrong

B)
P(-4,5) => P'(4,5) Wrong

C)
P(-4,-1) => P'(2,4) Wrong

D)
P(1,-5) => P'(-1,5) Correct

The answer is D.

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-x=-y+2 and 3y+4=2x solve using matrices

MissTica

$\begin{cases}-x=-y+2\\3y+4=2x\end{cases}\implies\begin{cases}x-y=-2\\2x-3y=4\end{cases}$

In matrix form, this is

$\begin{bmatrix}1&-1\\2&-3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-2\\4\end{bmatrix}$

The coefficient matrix has determinant

$\begin{vmatrix}1&-1\\2&-3\end{vmatrix}=-3+2=-1\neq0$

so it has an inverse, which is

$\begin{bmatrix}1&-1\\2&-3\end{bmatrix}^{-1}=\begin{bmatrix}3&-1\\2&-1\end{bmatrix}$

Multiply both sides by the inverse matrix:

$\begin{bmatrix}3&-1\\2&-1\end{bmatrix}\begin{bmatrix}1&-1\\2&-3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}3&-1\\2&-1\end{bmatrix}\begin{bmatrix}-2\\4\end{bmatrix}$

$\implies\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-10\\-8\end{bmatrix}$

so that $x=-10$ and $y=-8$ .

8 0

3 years ago

What is the slope of a line parallel to the line 2x + 3y = 5?

SOVA2 [1]

i think its 2/3 but im not sure .

6 0

3 years ago

Read 2 more answers

Nina and Luca were told to draw a net for the three-dimensional figure shown below. Which statement

elena55 [62]

Answer:

Step-by-step explanation:

7 0

2 years ago

A certain country's postal service currently uses 55-digit zip codes in most areas. how many zip codes are possible if there a

VashaNatasha [74]

There would be 100,000 if there are no restrictions on the digits and 90,000 if they cannot use 0 as the first digit.

If there are no restrictions, there are 10 possibilities for each digit:
10(10)(10)(10)(10) = 100,000

If the first digit cannot be 0, there are 9 possibilities for it and 10 possibilities for each of the other 4:
9(10)(10)(10)(10) = 90,000

8 0

3 years ago

What is the area?

balu736 [363]

Answer:

Solution given:

For rectangle

length [L]=BC=16in

breadth [b]=AB=4in

For traingle

length[l]=8in

breadth [b]=3in

total area =area of rectangle ABCD+2×area of triangle DEF

=L×b+2×1/2×[b×h]

=16×4+8×3=88in² is your answer

4 0

2 years ago