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
masya89 [10]
3 years ago
7

A,B and C are the vertices of one triangle.

Mathematics
2 answers:
dsp733 years ago
4 0

Answer:


Step-by-step explanation:

Given: The triangle with coordinate A(4,6), B(2,-2) and C(-2,-4). D is the mid point of AB and E is the mid point of AC.

To prove: DE is parallel to BC.

Construction: Join DE.

Proof: If we prove the basic proportionality theorem that is \frac{AD}{DB}=\frac{AE}{EC}, then it proves that DE is parallel to BC.

Now, Mid Point D has coordinates=(\frac{4+2}{2},\frac{6-2}{2})=(3,2) and Mid Point E has coordinates=(\frac{4-2}{2},\frac{6-4}{2})=(1,1)

Now, AD= \sqrt{(4-3)^{2}+(6-2)^{2}}=\sqrt{17}

DB=\sqrt{(3-2)^{2}+(2+2)^{2}}=\sqrt{17}

AE=\sqrt{(4-1)^{2}+(6-1)^{2}}=\sqrt{34}

EC=\sqrt{(1+2)^{2}+(1+4)^{2}}=\sqrt{34}

Now, \frac{AD}{DB}=\frac{AE}{EC}

=\frac{\sqrt{17}}{\sqrt{17}}=\frac{\sqrt{34}}{\sqrt{34}}=\frac{1}{1}

Hence, \frac{AD}{DB}=\frac{AE}{EC}

Thus, By basic proportionality theorem, DE is parallel to BC.

Goshia [24]3 years ago
4 0

Step-by-step explanation:

If DE and BC are parallel, then they have the same slope.

We have

A(4, 6), B(2, -2), C(-2, -4)

The formula of a midpoint:

\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)

D is the midpoint of AB, and E is a midpoint of AC.

Calculate the coordinateso fo D and E:

D\left(\dfrac{4+2}{2},\ \dfrac{6+(-2)}{2}\right)\to D\left(\dfrac{6}{2},\ \dfrac{4}{2}\right)\to D(3,\ 2)\\\\E\left(\dfrac{4+(-2)}{2},\ \dfrac{6+(-4)}{2}\right)\to E\left(\dfrac{2}{2},\ \dfrac{2}{2}\right)\to E(1,\ 1)

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

Calculate the formula of a DE and BC:

DE:\\\\m_{DE}=\dfrac{2-1}{3-1}=\dfrac{1}{2}\\\\BC:\\\\m_{BC}=\dfrac{-4-(-2)}{-2-2}=\dfrac{-4+2}{-4}=\dfrac{-2}{-4}=\dfrac{1}{2}

The slope DE and the slope BC are the same.

Therefore DE is parallel to BC.

You might be interested in
Help! open the attachment below!
gregori [183]

Answer:

yes it is

Step-by-step explanation:X=side lenghths 2/3

                                            Y=perimeter 12/18

2 time 6=12 and 3 times 6=18 and it is paraticly telling you

2/6 and 3/6 i beleve i need a lil more info

6 0
2 years ago
Solve by the method of balancing and equation and write the step use to separate the variable.....​
lesya [120]

Answer:

the required answers are :

c) x = 2

d) x = 27 / 7

e) x = 9

f ) x = 6

Step-by-step explanation:

for explanation see the attached image

^_^

5 0
3 years ago
How many times does 5.50 go into 60.50?
KatRina [158]
5.50 goes into 60.50 13.50 times
7 0
3 years ago
Read 2 more answers
Brainlest 5 starred and thanked daily if you get this correct<br> Try your hardest
mart [117]
The cycle number two is the answer
8 0
3 years ago
c. Write an expression to represent the length of a string in yards in terms of the string's length, x, in inches
jeka57 [31]

Answer:

Answer:

y = \frac{x}{36}y=

36

x

Step-by-step explanation:

Given

Length of string = x inches

Required

Determine the length in yards

Represent the equivalent length with y

Such that

y = x\ inchesy=x inches

Divide x by 36 to get equivalent in yards

y = \frac{1}{36} * xy=

36

1

∗x

y = \frac{x}{36}y=

36

x

Hence, the equivalent in yards is \frac{x}{36}

36

x

8 0
3 years ago
Other questions:
  • Someone help and I’ll help you thanks guys!<br> Hopefully someone remembers these
    7·1 answer
  • PLEASE PLEASE PLEASE HELP ME SOMEBODY PLEASE!! LAST QUESTION!! PLEASE??
    11·2 answers
  • 5% of what number is 12
    14·2 answers
  • Hanna charges an hourly babysitting fee of 6$ for two children,m 7$ for 3 children, and $8 for four or five children.
    8·1 answer
  • Write the following fractions as decimals. First 2 answer gets 40 points!!!!!
    10·2 answers
  • Solve for x.<br> -4 &lt; 11 - 3.2
    14·1 answer
  • You have a $20 phone card. Calls made using the card cost $.03 per minute to destinations in the United States and $.06 per minu
    13·1 answer
  • Determine whether the system of equations has one solution, no solution, or infinitely many solutions. 4x=10+4y and 2x-2y=15
    5·1 answer
  • Solve the formula s=4pi r^2 for r
    13·1 answer
  • Factories 5x+10 <br> Somebody please help
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!