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
Finger [1]
3 years ago
7

Find the length of each side of the triangle determined by the three points P1,P2, and P3. State whether the triangle is an isos

celes triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.)
P1=(−1,4);P2=(6,2);P3=(4,−5)
Mathematics
1 answer:
Tanya [424]3 years ago
7 0

Answer:

The triangle is both an Isosceles triangle and a right triangle.

Step-by-step explanation:

Given the vertices of a triangle.

$ P_{1} = (- 1, 4) $

$ P_{2} = (6, 2) $    and

$ P_{3} = (4, - 5) $

We find the distance between all the points to determine the length of each side of the triangle.

Distance between any two points, say, $ (x_1, y_1) $ and $ (x_2, y_2) $ is:

                                 $ \sqrt{\bigg ( \textbf{x}_{\textbf{2}} \hspace{1mm} \textbf{- x}_{\textbf{1}} \bigg )^{\textbf{2}} \textbf{+}   \bigg( \textbf{y}_{\textbf{2}} \hspace{1mm} \textbf{- y}_{\textbf{1}} \bigg)^ {\textbf{2}} $

Length between $ P_1 $ and $ P_{2} $ , (Side 1) :

$ (x_1, y_1) = (- 1, 4) $     and

$ (x_2, y_2) = (6, 2) $

Distance = $ \sqrt{\bigg(6 - (-1) \bigg)^{2} \hspace{1mm} + \hspace{1mm} \bigg( 2 - 4 \bigg )^2 $

$ = \sqrt{7^2 + 2^2} $

$ = \sqrt{49 + 4} $

$ = \sqrt{\textbf{53}} $

Length of Side 1 = $  \sqrt{\textbf{53}} $ units.

Distance between $ P_1 $ and P_2 , (Side 2):

$ (x_1, y_1) = (-1, 4) $

$ (x_2, y_2) = (4, - 5) $

Distance = $ \sqrt{ \bigg( 4 + 1 \bigg)^2 \hspace{1mm} + \bigg( - 5 - 4 \bigg ) ^2 $

$ = \sqrt{ 25 + 81 } $

$ = \sqrt{\textbf{106}} $

Length of Side 2 = $ \sqrt{\textbf{106}} $ units.

Distance between $ P_2 $ and $ P_3 $ , Side 3 :

$ (x_1, y_1) = (4, 5) $

$ (x_2, y_2) = (6, 2) $

Distance = $ \sqrt{ 2^2 \hspace{1mm} + \hspace{1mm} 7^2} $

$ = \sqrt{49 + 4} $

$ = \sqrt{\textbf{53} $

Length of Side 3  = $ \sqrt{\textbf{53}} $ units.

Note that the length of Side 1 = Length of Side 3.

That means the triangle is Isosceles.

Also, For a triangle to be right angle triangle, using Pythagoras theorem we have:

(Side 1)² + (Side 3)² = (Side 2)²

$ \bigg( \sqrt{53} \bigg )^2 \hspace{1mm} + \hspace{1mm} \bigg( \sqrt{53} \bigg)^2 \hspace{1mm} = \hspace{1mm} \bigg ( \sqrt{106} \bigg ) ^2 $

i.e, 53 + 53  = 106

Hence, the triangle is a right - angled triangle as well.

You might be interested in
This table shows the number of different sized pipes that have been used at Highfield Builders in January.
mote1985 [20]

Answer:

No

Mean diameter = 44, which is in the 40 - 44 cm group

Step-by-step explanation:

Given the data:

Diameter (cm) - mid point(X) - frequency(F) - - FX

35-39 - - - - 37 - - - - 8 - - 296

40-44 - - - 42 - - - 10 - - - 420

45-49 - - - 47 - - - 13 - - - 611

50-54 - - - 52 - - - 3 - - - 156

55-59 - - - 57 - - - 1 - - - 57

Mean of grouped data:

Sum of (F × X) / sum of F

1540 / 35 = 44

8 0
4 years ago
Two trains are traveling at a constant rate which train has the greater speed
notka56 [123]
Neither cause there both at the same constant rate so one train wouldn’t be traveling at a greater speed unless there is something missing from the question being asked like the actual speed of each individual train then there would be one train traveling at a greater speed
3 0
3 years ago
1)<br> Find the value of x.
Stells [14]

x=8

Explanation:

the opposite side is 72, which means I have to make 9x end up equaling 72.

72÷9

////

72/9

=8

9×8=72

<u>Therefore</u>

the value of x is 8.

6 0
2 years ago
3.7 + 1.13 X 2.9-5.5 =
Marta_Voda [28]

Answer:

Step-by-step is 1.477

8 0
3 years ago
Read 2 more answers
What is the solution the this equation? solve using linear combination method:
VARVARA [1.3K]
The solution is x=6 and y=5

6 0
3 years ago
Other questions:
  • which ordered pair would form a proportional relationship with the point graphed below. A.(-10,30). B.(30,-15). C. ( -30,10). D.
    8·2 answers
  • HELP HELP HELP HELP HELP
    13·2 answers
  • Can someone help please?
    8·2 answers
  • A teacher spends hour grading of a student's essay. At this rate, how long does it take the teacher to grade the student's entir
    12·1 answer
  • The two binomials (3x - 4) and (2x - 3) are the factors of which polynomial?
    11·1 answer
  • What dose -0.1c = -10 equal
    10·1 answer
  • Order from least to greatest
    11·2 answers
  • Pls help, i am giving brainliest out :)
    10·1 answer
  • ASAP!! DUE TOMORROW!<br><br> 8522/2<br><br> (SHOW UR WORK!,!)
    14·1 answer
  • Which expression is equivalent to y^4-400?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!