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
Eddi Din [679]
3 years ago
5

The vertices of ∆ABC are A(-2, 2), B(6, 2), and C(0, 8). The perimeter of ∆ABC is units is? What is the area?

Mathematics
2 answers:
11111nata11111 [884]3 years ago
4 0

we have

A(-2, 2),B(6, 2),C(0, 8)

see the attached figure to better understand the problem

we know that

The perimeter of the triangle is equal to

P=AB+BC+AC

and

the area of the triangle is equal to

A=\frac{1}{2}*base *heigth

in this problem

base=AB\\heigth=DC

we know that

The distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

Step 1

<u>Find the distance AB</u>

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

Substitute the values in the formula

d=\sqrt{(2-2)^{2}+(6+2)^{2}}

d=\sqrt{(0)^{2}+(8)^{2}}

dAB=8\ units

Step 2

<u>Find the distance BC</u>

B(6, 2),C(0, 8)

Substitute the values in the formula

d=\sqrt{(8-2)^{2}+(0-6)^{2}}

d=\sqrt{(6)^{2}+(-6)^{2}}

dBC=6\sqrt{2}\ units

Step 3

<u>Find the distance AC</u>

A(-2, 2),C(0, 8)

Substitute the values in the formula

d=\sqrt{(8-2)^{2}+(0+2)^{2}}

d=\sqrt{(6)^{2}+(2)^{2}}

dAC=2\sqrt{10}\ units

Step 4

<u>Find the distance DC</u>

D(0, 2),C(0, 8)

Substitute the values in the formula

d=\sqrt{(8-2)^{2}+(0-0)^{2}}

d=\sqrt{(6)^{2}+(0)^{2}}

dDC=6\ units

Step 5

<u>Find the perimeter of the triangle</u>

P=AB+BC+AC

substitute the values

P=8\ units+6\sqrt{2}\ units+2\sqrt{10}\ units

P=22.81\ units

therefore

The perimeter of the triangle is equal to 22.81\ units

Step 6

<u>Find the area of the triangle</u>

A=\frac{1}{2}*base *heigth

in this problem

base=AB=8\ units\\heigth=DC=6\ units

substitute the values

A=\frac{1}{2}*8*6

A=24\ units^{2}

therefore

the area of the triangle is 24\ units^{2}

malfutka [58]3 years ago
3 0
Best is to draw a sketch of the three points.
Next step is to find the distances BC, CD, DB.
The perimeter is the sum of the three distances.

The distances are found using the distance formula:
D=sqrt((y2-y1)^2+(x2-x1)^2)
<span>order of (x1,y1), (x2,y2) is not important.

Given A(2,8),B(16,2),C(6,2)
we calculate 
AB=sqrt((16-2)^2+(2-8)^2)=sqrt(14^2+6^2)=sqrt(232);
BC=sqrt((6-16)^2+(2-2)^2)=sqrt(10^2+0)=10
CA=sqrt((2-6)^2+(8-2)^2)=sqrt(4^2+6^2)=sqrt(16+36)=sqrt(52)

Perimeter=AB+BC+CA=32.443 units

For the area, we note that BC is horizontal (parallel to the x-axis), so 
area = (1/2)bast * height
=(1/2)10*(ya-yb)
=(1/2)10*(8-2)
=(1/2)10*6
=30 unit^2</span>
You might be interested in
Which of the ratio equivalent to 1:3 select all that apply
nekit [7.7K]

Answer:

4:12

6:18

8:24

Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number.

3 0
2 years ago
<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B2%7D%20%2B1%20%3D%20%5Csqrt%7B3%7D%20" id="TexFormula1" title=" \frac{x}{2
Tresset [83]
I hope this helps you

3 0
3 years ago
In a class of 40 students of the total number of students like to study English and of the total number of students like to stud
RUDIKE [14]

Answer:

10/100

Step-by-step explanation:

6 0
3 years ago
When is it best to review your notes
sergey [27]

As soon as possible after the lecture

5 0
3 years ago
Read 2 more answers
Can someone please help me I can’t afford to get anymore wrong
weeeeeb [17]
Vehicle B need fewer repairs on average, but the number of repairs per vehicle has greater variation
4 0
3 years ago
Other questions:
  • What is the answer for 35 3/4 - 1/8
    6·1 answer
  • When 5 is added to 2 times a number, the result is 45. find the number.
    14·1 answer
  • Find the value of the length <br> x<br> rounded to 1 DP.
    7·2 answers
  • Can Someone Please Help Me Out with My Math Homework!
    15·1 answer
  • The quotient is 71 2/3 what is the divisor
    7·2 answers
  • Samantha Cruz has 200 coins (quarters and dimes). She has $44.00. Write a system of equations and determine how many quarters= _
    13·1 answer
  • In the figure, ΔABC ∼ ΔDEF. Solve for x.  picture attached.
    13·2 answers
  • Question 19
    6·1 answer
  • Confusion plz help me.
    14·2 answers
  • The truth or falsity of a statement ?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!