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
anzhelika [568]
1 year ago
15

Without plotting points, let M=(-2,-1), N=(3,1), M'= (0,2), and N'=(5, 4). Without using the distanceformula, show that segments

MN and M'N' have the same length.
Mathematics
1 answer:
kramer1 year ago
7 0

Given:

M=(x1, y1)=(-2,-1),

N=(x2, y2)=(3,1),

M'=(x3, y3)= (0,2),

N'=(x4, y4)=(5, 4).

We can prove MN and M'N' have the same length by proving that the points form the vertices of a parallelogram.

For a parallelogram, opposite sides are equal

If we prove that the quadrilateral MNN'M' forms a parallellogram, then MN and M'N' will be the oppposite sides. So, we can prove that MN=M'N'.

To prove MNN'M' is a parallelogram, we have to first prove that two pairs of opposite sides are parallel,

Slope of MN= Slope of M'N'.

Slope of MM'=NN'.

\begin{gathered} \text{Slope of MN=}\frac{y2-y1}{x2-x1} \\ =\frac{1-(-1)}{3-(-2)} \\ =\frac{2}{5} \\ \text{Slope of M'N'=}\frac{y4-y3}{x4-x3} \\ =\frac{4-2}{5-0} \\ =\frac{2}{5} \end{gathered}

Hence, slope of MN=Slope of M'N' and therefore, MN parallel to M'N'

\begin{gathered} \text{Slope of MM'=}\frac{y3-y1}{x3-x1} \\ =\frac{4-(-1)}{5-(-2)} \\ =\frac{3}{2} \\ \text{Slope of NN'=}\frac{y4-y2}{x4-x2} \\ =\frac{4-1}{5-3} \\ =\frac{3}{2} \end{gathered}

Hence, slope of MM'=Slope of NN' nd therefore, MM' parallel to NN'.

Since both pairs of opposite sides of MNN'M' are parallel, MM'N'N is a parallelogram.

Since the opposite sides are of equal length in a parallelogram, it is proved that segments MN and M'N' have the same length.

You might be interested in
Math question down below
Elza [17]
The answer is 9 3/7 the last one
6 0
3 years ago
Read 2 more answers
Which expression is the same as 10÷4?
prisoha [69]
10/4 is not the simplified version that it can be. So 5/2 would be the same expression.
3 0
3 years ago
Read 2 more answers
Find the Mean, Median, Mode and Range of each series. Mean: 126 ÷ 9 = 14 1) 6 , 12 , 8 , 4 , 16 , 16 , 6 , 16 , 9 93 ÷ 9 2) 13 ,
Nadya [2.5K]

Answer:

129-14 is 115 than minus 6 than add 12

Step-by-step explanation:

7 0
3 years ago
X +3/ 5 = 2 <br> i need help
DochEvi [55]

This equation basically says that a number plus 3/5 equals 2 so we can simply:

2 - 3/5 = x

Therefore x equals 1 & 2/5 or 1.4

8 0
3 years ago
Jason's dad gave him a budget of $150 to spend on lacrosse equipment. How much will Jason have left over if he buys a helmet for
Yanka [14]
The answer is 2.99 explanation is that I used my calculator lol
7 0
3 years ago
Read 2 more answers
Other questions:
  • What is the following quotient? StartFraction StartRoot 6 EndRoot + StartRoot 11 EndRoot Over StartRoot 5 EndRoot + StartRoot 3
    8·2 answers
  • What does 18 2/3÷7 1/3 equal
    5·2 answers
  • Only 5-8 It’s Probability
    13·1 answer
  • Which of the following is the expansion of (2m - n)7?
    11·2 answers
  • PLEASE HELP ON MATH HOMEWORK
    5·1 answer
  • The mean consumption of bottled water by a person in the United States is 28.5 gallons per year. You believe that a person consu
    7·1 answer
  • Given: f(x) = x2, g(x) = x + 6, h(x) = 7<br> Find g{fſh(x)}}.<br> 20<br> 169<br> 55
    15·1 answer
  • Given the endpoint x(11,-2) and the midpoint (4,3) find the missing endpoint y. Write answer as order pair.
    5·2 answers
  • Find the missing angle ACB.<br> A. 90°<br> B. 70°<br> C. 45°<br> D. 40<br> E. 20°
    8·1 answer
  • 65% of what number is 39 then write an equation
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!