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
pashok25 [27]
2 years ago
7

1. Show that the triangle with vertices A (8,5). B (1, -2) and C(-3, 2) is a right angled triangle. Find its area.​

Mathematics
2 answers:
notka56 [123]2 years ago
5 0

Answer:

Step-by-step explanation: (1)

Given vertices are A(3,4), B(2,-1) and C(4,-6).

We need to calculate the length of the sides AB,BC,AC.

We have to distance formula which can tell the distance between 2 points.

d = √(x2 - x1)^2 + (y2 - y1)^2.

(1)

AB = √(2 - 3)^2 + (-1 - 4)^2

    = √(-1)^2 + (5)^2

    = √1 + 25

    = √26.

(2)

BC = √(4 - 2)^2 + (-6 + 1)^2

    = √(2)^2 + (5)^2

    = √4 + 25

    = √29

(3)

AC = √(4 - 3)^2 + (-6 - 4)^2

    = √(1)^2 + (-10)^2

    = √1 + 100

    = √101

Therefore, the length of the sides of the triangle are √26,√29 and √101.

----------------------------------------------------------------------------------------------------------

(2)

Let the given points be A(2,-2), B(-2,1) and C(5,2).

Using the distance formula,w e find that

⇒ AB = √(-2 - 2)^2 + (1 + 2)^2

        = √16 + 9

        = √25.

⇒ BC = √(5 + 2)^2 + (2 - 1)^2

         = √49 + 1

         = √50.

⇒ AC = √(5 - 2)^2 + (2 + 2)^2

         = √9 + 16

         = √25.

     

Now,

⇒ AB^2 + AC^2

⇒ (5)^2 + (5)^2

⇒ 25 + 25

⇒ 50.

⇒ (BC)^2.

Therefore, AB^2 + AC^2 = BC^2.

.

-BARSIC- [3]2 years ago
5 0

Answer:

  • 14 units²

Step-by-step explanation:

Plot the points.

According to the attached we can see the triangle is right.

<u>Use distance formula to find the length of AB and BC:</u>

  • AB=\sqrt{(1-8)^2+(-2-5)^2}=\sqrt{7^2+7^2}=7\sqrt{2}
  • BC=\sqrt{(-3-1)^2+(2+2)^2}=\sqrt{4^2+4^2}=2\sqrt{2}

<u>Find the area:</u>

  • A = 1/2(AB*BC)
  • A = 1/2(7\sqrt{2}*2\sqrt{2}) = 14

You might be interested in
You might need:
jonny [76]
The answer is 37, you add up all the numbers and divide whatever number you got by the amount of numbers there are :)
8 0
3 years ago
X= b- cd for c please solve and show work
SVETLANKA909090 [29]

Answer:

c=b-x/d hope it helps..............

8 0
2 years ago
The sum of two numbers is 82. The larger number is eight less then five times the smaller number. What are the numbers?
bonufazy [111]

Answer:

The smaller Number = 15

The larger number = 67

Step-by-step explanation:

Let

The smaller number = x

The larger number = 5x - 8

The sum = 82

(5x - 8) + x = 82

5x - 8 + x = 82

6x - 8 = 82

Add eight to both sides

6x - 8 + 8 = 82 + 8

6x = 90

Divide both sides by 6

x = 90/6

= 15

Therefore,

The smaller number = x = 15

The larger number = 5x - 8

= 5(15) - 8

= 75 - 8

= 67

6 0
3 years ago
Question 2 help me on the table
Alexxandr [17]
I THINK on b its that the percentages represent........................................................................................................................................READY.............UMMMMM............HOW MANY POEPLE GET A JOB ON HONEROLL OR TRY TO GET A JOB WHEN ITS HONNER ROLL OR NOTTTTTTTTTTTTTTTT.............................there u go........................byeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
3 0
3 years ago
What is the vertex and the equation of the axis of symmetry of the graph of y=x2-6x-7?
Ray Of Light [21]
X= -b over 2a = --6 over 2×1=3
y=3²-6(3)-7=-16
vertex is (3,-16)
axis of symmetry is 3
3 0
3 years ago
Read 2 more answers
Other questions:
  • Please do this quick!
    9·1 answer
  • Sketch the asymptotes and graph the function y=6/(x-2)+4
    11·2 answers
  • A small college has 36 math majors, 78 engineering majors , and 156 business majors in its graduate programs. What’s is the rati
    12·1 answer
  • Write an equation that represents each mixed number as a sums of a whole number and unit fractions 4 1/4 and 1 5/6
    13·1 answer
  • A radio station gives free tickets to 10% of the people attending a concert. The radio station gives 640 people free tickets. Wh
    9·1 answer
  • A circle with radius of 6cm sits inside a circle with a radius of 9cm. What is the area of the shaded region?
    6·2 answers
  • Please help me....................
    7·1 answer
  • Help<br> ===================
    13·1 answer
  • 8 less a number is less than or equal to 17
    14·2 answers
  • Which statement is true?​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!