Determine the point of intersection of right bisectors in a triangle ∆ABC with vertices A (-3, 5), B (1, 1) and C (−7, −3). Find the distance from the point of intersection to each vertex of the triangle.
Answers
9514 1404 393
Answer:
intersection: (-3 2/3, 1/3)distances to vertices: (10/3)√2Step-by-step explanation:
A) In order to write the equations of the perpendicular bisectors of the segments, we need to know the midpoint and the slope.
The midpoint is the average of the coordinates:
midpoint(A, B) = ((-3, 5) +(1, 1))/2 = (-3+1, 5+1)/2 = (-1, 3)
midpoint(A, C) = ((-3, 5) +(-7, -3))/2 = (-3-7, 5-3)/2 = (-5, 1)
The differences between the coordinates of the points can be helpful:
B-A = (1, 1) -(-3, 5) = (1+3, 1-5) = (4, -4) . . . . . reduces to (∆x, ∆y) = (1, -1)
C-A = (-7, -3) -(-3, 5) = (-7+3, -3-5) = (-4, -8) . . . . . reduces to (∆x, ∆y) = (1, 2)
_____
A line through point (h, k) perpendicular to one with (∆x, ∆y) can be written:
(∆x)(x -h) +(∆y)(y -k) = 0
Then the bisectors of AB and AC will be ...
(x +1) -(y -3) = 0
(x +5) +2(y -1) = 0
Their intersection point can be found by solving this system.
(x +2y +3) -(x - y + 4) = (0) -(0) . . . . . subtract the 1st equation from the 2nd
3y -1 = 0
y = 1/3
x = y -4 = -3 2/3
The point of intersection of the right bisectors is (x, y) = (-3 2/3, 1/3).
__
B) The intersection point is the circumcenter. It will be the same distance from any of the vertices.
That distance can be found using any of the vertices. Using point B, we find the distance to be ...
d = √((-3 2/3 -1)^2 +(1/3 -1)^2) = √((14/3)^2 +(2/3)^2) = √(200/9)
d = (10/3)√2
The distance to each vertex is (10/3)√2 ≈ 4.71.
Related Questions
A wire 45 meters long is cut into two pieces, One piece is 5 meters longer than the other. What is the length of the two pieces? Create an equation and solve .
Answers
Given:
A wire 45 meters long is cut into two pieces
One piece is 5 meters longer than the other.
To find:
The length of the two pieces.
Solution:
Let length of one piece be x.
One piece is 5 meters longer than the other. So,
Length of another piece = x+5
Total length of wire is 45. So,
[tex]x+(x+5)=45[/tex]
[tex]2x+5=45[/tex]
Subtract 5 from both sides.
[tex]2x=45-5[/tex]
[tex]2x=40[/tex]
Divide both sides by 2.
[tex]x=\dfrac{40}{2}[/tex]
[tex]x=20[/tex]
Now,
Length of one piece = 20 meters
Length of another piece = 20 + 5
= 25 meters
Therefore, the length of two pieces are 20 and 25 meters.
What is the slope of the line through (3,7) and (-1,4)
Answers
Answer:
[tex]m=\frac{3}{4}[/tex]
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (3, 7)
Point (-1, 4)
Step 2: Solve for slope m
Substitute: [tex]m=\frac{4-7}{-1-3}[/tex]Subtract: [tex]m=\frac{-3}{-4}[/tex]Simplify: [tex]m=\frac{3}{4}[/tex]Answer:
4/3
Step-by-step explanation:
Use the formula rise/run. But first, if you plot this on a graph, (-1,4) will come first because its x value is smaller. So, for this, let's look at (-1,4) first.
To get from -1 to 3, you must rise 4 units. To get from 4 to 7, you must run 3 units.
So, if you put this together, you will get 4/3!
Hope I helped!!!!
simplify the expression: 3x + 5 + 7x=
Answers
The answer would be 10x + 5
Hello!
The answer is 10x + 5!
Hopefully this helps! <3 ^^
Whats a negative number that has an absolute value greater than 10
Answers
Answer:
-11
Step-by-step explanation:
Absolute value means the distance from 0 so in this case, anything that is 10+ from 0 will work
Answer:
-11
Step-by-step explanation:
The absolute value of -11 is 11, and that is greater than 10.
I hope you enjoyed the answer, and if it was helpful, please mark this as brainliest! Thank you! :)
please help me there are more questions after this.
Answers
Given ΔDEF : ΔRST, find x. 12 15 16 64
Answers
Answer:
12
Step-by-step explanation:
For ΔDEF similar to ΔRST, the value of x is 12. So, option a) is correct.
Two triangles are said to be similar if corresponding angles are equal or corresponding sides are in the same proportion.
Given triangles are similar:
ΔDEF ~ ΔRST
Therefore, using the property of similar triangle that corresponding sides of a similar triangle are in same proportion.
[tex]\dfrac{EF}{ST}=\dfrac{ED}{SR}\\\\\dfrac{x}{16}=\dfrac{3}{4}\\\\x=\dfrac{3}{4}\times 16\\\\x=12[/tex]
Thus, the value of x is 12. So, option a) is correct.
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Find an equation for the line below in y=mx+b
Answers
Answer:
y = -1/2x - 11/2
Step-by-step explanation:
Using slope intercept form y = mx + b, to determine the equation, first count the rise(vertical or change in y), and run(horizontal or change in x) of the line.
m is the slope, b is the y-intercept which will remain when x is 0 as this will cancel out the m.
Be careful when determining the slope, and pay attention to the steps(count) of the x, and y axis.
As this graph measures a line with a negative slope passing through the y axis at -5 1/2 → -11/2, with a step of 1, we can count the squares normally to determine the slope.
So since we know that this line has two obvious points (-5,-3) and (1,-6) we can use the equation for slope to measure it's steepness.
m = y2-y1/x2-x1
with (x1,y1) being the first point, and (x2,y2) being the second point.
So: (negative minus a negative makes a positive)
m = -6-(-3)/1-(-5) = -6 + 3/ 1 + 5 = -3/6 = -1/2.
Since m = -1/2, and b = -11/2, the line must be y = -1/2x - 11/2.
someone please explain
Answers
Explain what? What would you like help with? :)
Answer:
whats ur question
Step-by-step explanation:
HELP!!!!!!!!!!!!!! I ONLY HAVE 5 MIN TO TURN THIS IN!!!!
Answers
Answer:
I think A but I might be wrong
Which equation represents a line parallel to ?
A. 2x-4y=28
B. 4x+2y=10
C. 4x-2y=10
D. 2x+4y=10
Answers
Answer:
b
Step-by-step explanation:
Why is it impossible to represent a vertical line using the slope-intercept form and the point-slope form of a linear equation?
Answers
Answer:
Both equations include the slope, which is undefined for a vertical line.
Step-by-step explanation:
it just is lol
What is the answer to this equation? -(x-10)=7
Answers
Answer:
x=3
Step-by-step explanation:
-(x-10)=7
-x+10=7
-x=-3
x=3
-(3-10)=7
11-11-29 Daily work ( Go math 4.3)
Answers
Plzz help!!!
What is the value of both these problems?
Answers
Problem 2
We have an isosceles triangle because of the two congruent sides (21 each).
The angles opposite the congruent sides are known as the base angles, and the base angles are congruent. For now, we don't know what they are. They are both x. I recommend writing 'x' onto the diagram where that missing unmarked angle is.
Then we'll use the idea that all three angles of any triangle always add to 180
x+x+38 = 180
2x+38 = 180
2x = 180-38
2x = 142
x = 142/2
x = 71
Answer: Choice A) 71=======================================================
Problem 3
We use the same ideas as the previous problem. This time the base angles are 56 degrees each. The remaining angle is x.
x+56+56 = 180
x+112 = 180
x = 180-112
x = 68
Answer: Choice A) 68whats the slope for (-2,4) and (10, -2)
Answers
Answer:
-1/2
Step-by-step explanation:
y2-y1 over x2-x1
-2-4 over 10+2
which equals -6/12
which simplifies to -1/2
Answer:
-1/2
Step-by-step explanation:
Slope formula- m = y2 - y1
x2 - x1
x1,y1
-2, 4
x2,y2
10,-2 -2 - 4
10 - (-2) = -6/12 = -1/2
Find the distance between the two points in simplest radical form.
(8, -3) (6, -8)
Answers
Answer:
[tex]d = \sqrt{29}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra II
Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point (8, -3)
Point (6, -8)
Step 2: Find distance d
Substitute: [tex]d = \sqrt{(6-8)^2+(-8+3)^2}[/tex]Subtract/Add: [tex]d = \sqrt{(-2)^2+(-5)^2}[/tex]Exponents: [tex]d = \sqrt{4+25}[/tex]Add: [tex]d = \sqrt{29}[/tex] Fedex typically deleviers 2,400 packages per day and uses 75 trucks for delivery. If the number of trucks used per day is proportional to the number of packages delivered, how many packages would be delivered if there are 100 trucks avilable?
A 3.200 packages
B 1.800 packages
Answers
Answer:
A
Step-by-step explanation:
What is the constant of proportionality
Answers
Answer:
It is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate.
Step-by-step explanation:
Please help with this assignment
Answers
Answer:
3
Step-by-step explanation:
Answer:
24 yards long
PLA HELP ME 100 POINTS FOR TO ANSWER
The slope of a line is 2. The y-intercept of the line is –6. Which statements accurately describe how to graph the
function?
O Locate the ordered pair (0, -6). From that point on the graph, move up 2, right 1 to locate the next ordered pair or
the line. Draw a line through the two points.
O Locate the ordered pair (0, -6). From that point on the graph, move up 2, left 1 to locate the next ordered pair on
the line. Draw a line through the two points.
O Locate the ordered pair (-6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair on
the line. Draw a line through the two points.
O Locate the ordered pair (-6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair on
the line. Draw a line through the two points.
Answers
Answer: A
Step-by-step explanation: e2020
Answer:
one
Step-by-step explanation:
This is actually really confusing please help me out.
Answers
Answer:
a ball bouncing off a wall
Step-by-step explanation:
Thomas went to the store to buy video games for $13.50 each and controllers that cost $55 each and controllers. the total amount that Thomas spent can be represented by c=13.50+p, where c is the total cost, g is the number of games he bought, and p is the cost of the controllers. the controllers cost $55 and Thomas spent $136 total
Answers
Answer:6 games
Step-by-step explanation:
Thomas spent a total of 136 dollars so you subtract 55 from 136 and divide by 13.50 to get 6.
4 2/3 miles in 3/4 hour
4/23 divided by 3/4 ?
NEED FAST ANSWERS !
Answers
Answer:
= 12 miles per hour
Step-by-step explanation:
This is a fraction equal to
30 miles ÷ 2.5 hours
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 2.5
30 miles ÷ 2.5
2.5 hours ÷ 2.5
=
12 miles
1 hour
=
12 miles
hour
= 12 miles per hour
In a company, 95% of the workers are men. If 125 people work for the company who aren't men , how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
ill give you brainliesttttt
Answers
Based on the percentage of men workers in the company, the total number of workers is 2,500.
What is the percentage?The percentage is the fractional value of a variable concerning another.
Percentages are like ratios and proportions, which show the numerical relationship between the independent and dependent variables.
The percentage of men workers = 95%
The number of non-men workers = 125
The percentage of non-men workers = 5% (1 - 95%)
If 5% of the workers are 125, the total number of workers, 100% = 2,500 (125/5% x 100%).
Check:
Men workers = 95% = 2,375
Non-men workers = 5% = 125
Total = 2,500
Thus, given the percentage of men workers as 95%, the total number of workers in the company is 2,500.
Learn more about percentages at brainly.com/question/24877689
The total number of workers in the company is 2,500.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
In a company, 95% of the workers are men.
125 people work for the company who aren't men.
We need to find number of workers working in the company.
The percentage of men workers = 95%
The number of non-men workers = 125
The percentage of non-men workers = 5% (1 - 95%)
Men workers = 95% = 2,375
Non-men workers = 5% = 125
If 5% of the workers are 125
the total number of workers, 100% = 2,500 (125/5% x 100%).
Total = 2,500
Thus, given the percentage of men workers as 95%, the total number of workers in the company is 2,500.
Hence the total number of workers in the company is 2,500.
To learn more on Percentage click:
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Find the value of 4x2 – 2y when x = 3 and y = 2.
Answers
Answer:20
Step-by-step explanation:
4(3)2-2(2)
12(2)-4
24-4=20
can somebody help me with this please.
Answers
I don't know what number 1 and number 2 mean,
3：11
4
5：-3
6：-8
You can find the answer below. Among the questions I answered correctly, I hope to adopt it at the end. Thank you. Have a nice day.
There are 25 students in Ms. Nguyen’s second grade class. In the class election, 4 students Voted for Benjamin, 12 voted for Sahil, and 9 voted for Maria.
What percent of the class voted for Maria
Answers
Answer:
36%
Step-by-step explanation:
im having trouble figuring out what this question means |7| + -4=?
Answers
Answer:
3
Step-by-step explanation:
It means absolute value 7 plus -4
This means that if it were a -7, it would become positive because it is under absolute value bars...since it is positive nothing changes
7-4= 3
Please help I really need it I am in a timed test I will choose brainliest!
Write the standard form of the equation of a line with a slope of -4 passing through the point (1, -4).
Select one:
a. -4x - y = 0
b. -x - 4y - 15 = 0
c. x + 4y + 15 = 0
d. 4x + y = 0
Answers
I think the answer is a.
Step 1: We must determine the equation of the line in slope-intercept form* by solving for b.
[tex]-4 = -4(1) + b\\\\-4 = -4 + b\\\\0 = b[/tex]
Step 2: Now we write the equation in slope-intercept form.
[tex]y = -4x[/tex]
Step 3: We can now change the above equation to standard form by moving variables to one side.
[tex]y = -4x\\\\4x + y = 0[/tex]
Our answer is D. 4x + y = 0.
*Slope-intercept form: y = mx + b.
A car with a mass of 500 kg is accelerating at 10 m/s². What is the force being applied the car’s engine?
Answers
Answer:
M=500kg
a=10m/s^2
By formular:
F=ma
F=500*10
F=5000N