1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
White raven [17]
3 years ago
14

What is the equation for the line of reflection that maps the trapezoid onto itself?

Mathematics
2 answers:
snow_lady [41]3 years ago
6 0

The equation for the line of reflection which maps the trapezoid onto itself is \fbox{\begin\\\ \math y=2\\\end{minispace}}.

Further explanation:

From the given figure it is observed that there is a trapezoid placed vertically and the corner points of the trapezoid are (-2,7),(-2,-3),(2,0) and (2,4).

Label the point (-2,7) as A, (-2,-3) as B, (2,0) as C and (2,4) as D.

Figure 1 (attached in the end) shows the trapezoid ABCD.

From the given graph it is observed that the length of the side AB is 10\ \text{units}, length of side CD is 4\ \text{units}.

The line of reflection is a line which reflects the image of an object onto the other side in such a way that the reflected image is same as the original object.

For a regular polygon the line of reflection is the line of symmetry.

This implies that the line of symmetry for the given trapezium is its line of reflection.

A line of symmetry of a figure is a line which divides a figure into exactly two halves such that they can even overlap with each other.

For the given trapezium if we consider the line of symmetry as a vertical line then it is observed that any vertical line which cuts the trapezoid in two parts never gives two symmetrical halves.

From figure 2 (attached in the end) it is observed that any vertical does cut the trapezoid into two symmetrical halves.

The length of the side AB is 10\ \text{units} and the length of the side CD is 4\ \text{units}.

The coordinate of point A is (-2,7) and the coordinate for point B is (-2,-3).

As per the mid-point theorem the mid-point of a line joining the point (x_{1},y_{1}) and (x_{2},y_{2}) is calculated as follows:

\fbox{\begin\\\ \math (x,y)=\left(\frac{(x_{1}+x_{2})}{2},\frac{(y_{1}+y_{2})}{2}\right)\\\end{minispace}}

The coordinate of midpoint of AB is calculated as follows:

\begin{aligned}(x,y)&=\left(\frac{-2-2}{2},\frac{7-3}{1}\right)\\&=(-2,2)\end{aligned}

Therefore, the coordinate of midpoint of AB is (-2,2).  

The coordinate of point C is (2,0) and the coordinate for point D is (2,4).

The coordinate of midpoint of CD is calculated as follows:

\begin{aligned}(x,y)&=\left(\frac{2+2}{2},\frac{0+4}{2}\right)\\&=(2,2)\end{aligned}

Therefore, the coordinate of midpoint of CD is (2,2).

From the above calculation and the given graph it is concluded that the line y=2 divides the sides AB and CD into two halves.

From figure 3 (attached in the end) it is observed a right angle triangle is formed as \triangle \text{ADE}.

By using the Pythagoras theorem the length of AD is calculated as follows:

\begin{aligned}\text{AD}&=\sqrt{4^{2}+3^{2}}\\&=\sqrt{16+9}\\&=\sqrt{25}\\&=5\end{aligned}

Similarly, for \triangle \text{BCF} the length of BC is calculated as follows:

\begin{aligned}\text{BC}&=\sqrt{4^{2}+3^{2}}\\&=\sqrt{16+9}\\&=\sqrt{25}\\&=5\end{aligned}

This implies that the sides AD and BC are equal in length.

Since, the length of the side AD and BC are equal so the line y=2 will divide the trapezoid into two symmetrical halves in such a way that the two halves completely overlap with each other.

As stated above line of reflection for a regular polygon is its line of symmetry.

This implies that the line y=2 is the line of reflection for the trapezoid ABCD.

From figure 4 it is observed that the line y=2 is the line of symmetry for the trapezoid ABCD.

Therefore, the equation of line of reflection for the trapezoid is \fbox{\begin\\\ \math y=2\\\end{minispace}}.

Learn more:  

1. A problem to complete the square of quadratic function brainly.com/question/12992613  

2. A problem to determine the slope intercept form of a line brainly.com/question/1473992

3. Inverse function brainly.com/question/1632445  

Answer details  

Grade: Middle school  

Subject: Mathematics  

Chapter: Coordinate geometry

Keywords: Geometry, coordinate geometry, reflection, symmetry, polygon, line of reflection, line of symmetry, mid-point theorem, trapezoid, map trapezoid onto, equation, y=2, regular polygon, reflection of trapezoid.

Naya [18.7K]3 years ago
5 0

Answer:

x = 2

Explanation:

A line of reflection that maps a polygon onto itself will be a line of reflectional symmetry in the figure.

A line of reflectional symmetry is a line through which a figure can be folded in half.  For this trapezoid, a line of reflectional symmetry must be a perpendicular bisector of both bases.

This means in this figure, the line must be horizontal and must run at x = 2.

You might be interested in
Loretta’s income last year was $81,300. She made $56,800 at her salaried job and had additional passive income. If Loretta earne
aalyn [17]

Answer:

Option a.  $2,040

Step-by-step explanation:

step 1

To find out the amount of the additional passive income last year, subtract the amount earned at her salaried job from Loretta’s income last year

so

\$81,300-\$56,800=\$24,500

step 2

Divide the additional passive income last year by 12 (number of months in a year)

\$24,500/12=\$2,041.67

therefore

approximately $2,400 per month

5 0
2 years ago
Read 2 more answers
Identify the variable and the constant in the expression below. n + 3 variable: ___________________________ constant: __________
Ilya [14]
N is the variable and 3 is the constant.
8 0
2 years ago
the function p(t)=350e^-.2t represents the population of a city, in thousands, t years after 2010. determine the population of t
mezya [45]
350×e^(0.2×4)
=778.9393249724
4 0
2 years ago
26.48 divided by 2 and the method
e-lub [12.9K]

Answer:

13.24

Step-by-step explanation:

If you put it into the calculator, you get the answer. Or you could do long division, but that's difficult for no reason. You could also divide each number individually by 2, as they are all even, so that works too.

Hope this helps!

7 0
2 years ago
US$ 54000 is to be shared among Al, Bob and Chad in the ratio of 2: 3: 4. How much will Bob get?
Galina-37 [17]

Answer: If he gives Al 42, then he gives Bob 21 and Carl 84. Do those add up to 210? 42 + 21 + 84 = 147–that’s too small! Go bigger.

Step-by-step explanation:

So Since (D) is odd, shoot right to (E). If he gives Al 60, then he gives Bob 30 and Carl 120. Does that add up to 210? Yes, yes it does. 60 + 30 + 120 = 210.

6 0
2 years ago
Other questions:
  • Write to show how you make a ten. then add.
    13·1 answer
  • Number 17... please help!
    15·1 answer
  • Complete the following proof.<br> Given: m ∠XOY = m ∠WOV<br> m YZ = m ZW<br> Prove: m XZ = m ZV
    9·2 answers
  • 84 of %300. i somehow got 24 but the answer was something like 252, i dont really get how. can you help?
    8·2 answers
  • I only need the answer
    10·1 answer
  • A fair had been running in the town of Ajax for 2 years. The first year 15,754 people attended. The second year, 17,934 people a
    14·2 answers
  • To celebrate her birthday, Whitney wants to take her friends adventuring in a 4WD vehicle from All Terrain Tours.
    13·1 answer
  • What is the opposite of 8.5?
    13·1 answer
  • Find the following limit without using a graphing calculator or making a table.
    15·1 answer
  • Karen wants to place a lamp halfway between the
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!