Help me solve these problems please

The coordinates of the vertices of ΔPQR are (–2, –2), (–6, –2), and (–6, –5).

melamori03 [73]

<h3>Answer:</h3>

Yes, ΔPʹQʹRʹ is a reflection of ΔPQR over the x-axis

<h3>Explanation:</h3>

The problem statement tells you the transformation is ...

... (x, y) → (x, -y)

Consider the two points (0, 1) and (0, -1). These points are chosen for your consideration because their y-coordinates have opposite signs—just like the points of the transformation above. They are equidistant from the x-axis, one above, and one below. Each is a <em>reflection</em> of the other across the x-axis.

Along with translation and rotation, <em>reflection</em> is a transformation that <em>does not change any distance or angle measures</em>. (That is why these transformations are all called "rigid" transformations: the size and shape of the transformed object do not change.)

An object that has the same length and angle measures before and after transformation <em>is congruent</em> to its transformed self.

So, ... ∆P'Q'R' is a reflection of ∆PQR over the x-axis, and is congruent to ∆PQR.

6 0

3 years ago

Pigeon Hole Principle :

yaroslaw [1]

Answer:

A proof can be as follows:

Step-by-step explanation:

Let $S=\{a_{1},a_{2},...,a_{n},a_{n+1}\}$ be a set of $n+1$ integers. By the division algorithm the possible remainders when we divide by $n$ are $0,1,2,....,n-1$ . Then, each integer $a_{i}\in S$ can be written as:

$a_{i}=np_{i}+r_{i},\,\,0\leq r_{i}$

Observe that the set of remainders $\{r_{1},r_{2},...,r_{n+1}\}$ has $n+1$ elements and each element has $n$ possible values. By the Pigenhole principle at least two remainders have the same value. Suppose that this two elements are $a_{i}, a_{j}$ . Then,

$\begin{array}{c}a_{i}=np_{i}+r\\a_{j}=np_{j}+r\end{array}$

Where $r_{i}=r_{j}=r$ . Then, $a_{i}-a_{j}=np_{i}-np_{i}=n(p_{i}-p_{j})$ . Then we have that $n$ divides $a_{i}-a_{j}$ .

5 0

3 years ago

A large soda-pop manufacturer wants to introduce a new design for the label on one of its signature soda-pop drinks. The manufac

hoa [83]

Answer:

This variation is a source of

response error.

Step-by-step explanation:

A response error shows the lack of accuracy in the customer responses to the survey questions. A response error can be caused by a questionnaire that requires framing improvements, misinterpretation of questions by interviewers or respondents, and errors in respondents' statements. Some responses are influenced by the answers provided to previous questions, which introduces response bias.

4 0

2 years ago

The vertices of triangle PQR are P(10,-6), Q(6,2), & R(4,-1). Describe a translation that places the image of the triangle e

Gnoma [55]

Answer:

Translate 7 units up and then translate 11 units to the left.

Step-by-step explanation:

We have the triangle PQR having co-ordinates (10,6), (6,2) and (4,-1).

It is required to translate ΔPQR so that the resulting image is completely inside the 2nd quadrant.

So, for that we will apply the following sequence of translations:

1. Translate 7 units up.

This will give us the figure in the 1st quadrant having co-ordinates (10,1), (6,9) and (4,6).

2. Translate 11 units to the left

We will get the final triangle P'Q'R' with the co-ordinates P'(-1,1), Q'(-5,9) and R'(-7,6) as shown below.

5 0

3 years ago

Prove LMNO is a parallelogram

Arturiano [62]

LMNO is a parallelogram because it has all 4 sides parallel to each other.

3 0

2 years ago

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