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
Lady bird [3.3K]
3 years ago
9

The centroid of a triangle is at (8, 7). One vertex of the triangle is at (0, 1). What is the midpoint of the side opposite this

vertex?
Mathematics
1 answer:
RideAnS [48]3 years ago
7 0

Answer:

(12,10)

Step-by-step explanation:

Let the midpoint of the side opposite this vertex have coordinates B(a,b)

We have the centroid at C(8,7) and the vertex of the triangle at A(0,1).

The centroid divides AB internally in the ratio 2:1

We use the formula:

(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})

where m:n=2:1 is the ratio of internal division.

We substitute the coordinates of A and B and the ratio to get:

(\frac{2a+1*0}{2+1},\frac{2b+1*1}{2+1})

This should simplify and give us the centroid.

(\frac{2a}{3},\frac{2b+1}{3})=(8,7)

This implies that:

\frac{2a}{3}=8,\frac{2b+1}{3}=7

We solve for a and b

2a=24,2b+1=21

a=12,b=10

Therefore the midpoint of the side opposite this vertex is (12,10)

You might be interested in
Leena loves peanut butter. today, she ate four tablespoons of it. if there are 6 mg of vitamin e in four tablespoons of peanut b
velikii [3]
<span>First, we need to know that the current recommended daily allowance of Vitamin E is 15 milligrams. If Leena ate four tablespoons of peanut butter, thus receiving only 6 milligrams, then we can determine the percentage by first dividing 100 into 15 parts (which gives us 6.66), and then multiply that answer by 6 (6 x 6.66), which gives us precisely 40. Thus, the answer is 40 percent.</span>
5 0
2 years ago
In the above figure, the radius of curvature is 10 ft and the height of the segment is 2 ft. What's the length of the chord?
Kay [80]
The answer is 12. I am 1,000,000% positive that it is the correct answer

4 0
3 years ago
What frcation is equal to 4​
Korolek [52]
The answer is D
Explanation 4 ones is 4
5 0
2 years ago
Which of the following is the equation logx4=-2 written in exponential form
maksim [4K]
X^-2=4. You got it correct:)
4 0
2 years ago
The temperature of a pot of water was 180.3°F and it cooled at a rate of -2.5°F for a minute after 20 minutes what was the tempe
kykrilka [37]
Temperature after 20 minutes is found by multiplying-2.5 by 20 since it goes down by 2.5 degrees for one minute. -2.5 * 20 = -50. Adding this to 180.3 will give the temperature 130.3 degrees.
7 0
2 years ago
Other questions:
  • It takes 2 people 20 minutes to install 8 tires on 2 vehicles. How many tires can 4 people load in one hour?
    10·1 answer
  • Show by using "proof by contradiction" that the set of binary sequences {0,1}N is uncountable.
    10·1 answer
  • At a clothing store, Ted bought 4 shirts and 2 ties for a total price of $95. At the same store, Steph bought 3 shirts and 3 tie
    10·1 answer
  • Please Help will give Brainliest!!
    15·1 answer
  • Plz help me quick!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    10·1 answer
  • Scores on the GRE (Graduate Record Examination) are normally distributed with a mean of 579 and a standard deviation of 94. Use
    13·1 answer
  • If f(x) = 5x2 − 2x, 0 ≤ x ≤ 3, evaluate the Riemann sum with n = 6, taking the sample points to be right endpoints. R6 =
    13·1 answer
  • Two functions are defined as shown. f(x) = - x -2 g(x) = -1 Which graph shows the input value for which f(x) = g(x)? ​
    15·1 answer
  • Mark sorted a set of shapes into two different categories. Explain, what two attributes were used to sort the shapes. help pleas
    15·1 answer
  • how do i find the type of relationship of a table? whether it is linear or quadradic and how do i find the formula for either re
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!