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olga_2 [115]
2 years ago
15

Giving brainliest whoever answers this question first, please help

Mathematics
1 answer:
vladimir2022 [97]2 years ago
6 0
The question is there
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Triangle ABC has vertices at A(2,3),B(-4,-3) and C(2,-3) find the coordinates of each point of concurrency.
dem82 [27]

Answer:

Circumcenter =(-1,0)

Orthocenter =(2,-3)

Step-by-step explanation:  

Given : Points A = (2,3), B = (-4,-3), C = (2,-3)  

Formula used :  

→Mid point of two points- (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

→Slope of two points - \frac{y_2-y_1}{x_2-x_1})

→Perpendicular of a line = \frac{-1}{slope of line})

Circumcenter- The point where the perpendicular bisectors of a triangle meets.

Orthocenter-The intersecting point for all the altitudes of the triangle.

To find out the circumcenter we have to solve any two bisector equations.

We solve for line AB and AC

So, mid point of AB =(\frac{2-4}{2},\frac{3-3}{2})=(-1,0)

Slope of AB =\frac{-3-3}{-4-2}=1

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of the perpendicular bisector = -1  

Equation of AB with slope -1 and the coordinates (-1,0) is,  

(y – 0) = -1(x – (-1))  

y+x=-1………………(1)  

Similarly, for AC  

Mid point of AC = (\frac{2+2}{2},\frac{3-3}{2})=(2,0)

Slope of AC = \frac{-3-3}{2-2}=\frac{-6}{0}  

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of the perpendicular bisector = 0  

Equation of AC with slope 0 and the coordinates (2,0) is,  

(y – 0) = 0(x – 2)  

y=0 ………………(2)  

By solving equation (1) and (2),  

put y=0 in equation (1)

y+x=-1

0+x=-1

⇒x=-1  

So the circumcenter(P)= (-1,0)

To find the orthocenter we solve the intersections of altitudes.

We solve for line AB and BC

So, mid point of AB =(\frac{2-4}{2},\frac{3-3}{2})=(-1,0)

Slope of AB =\frac{-3-3}{-4-2}=1

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of CF = -1  

Equation of AB with slope -1 and the coordinates (-1,0) gives equation CF  

(y – 0) = -1(x – (-1))  

y+x=-1………………(3)  

Similarly, mid point of BC =(\frac{-4+2}{2},\frac{-3-3}{2})=(-1,-3)

Slope of AB =\frac{-3+3}{-4-2}=0

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of AD = 0

Equation of AB with slope 0 and the coordinates (-1,-3) gives equation AD

(y-(-3)) = 0(x – (-1))  

y+3=0

y=-3………………(4)  

Solve equation (3) and (4),

Put y=-3 in equation (3)

y+x=-1

-3+x=-1

x=2

Therefore, orthocenter(O)= (2,-3)


7 0
3 years ago
49767269 x 327686000 - 1029 + 1101 / 32
mars1129 [50]

Answer:

16308037309533006\frac{13}{32}

Step-by-step explanation:

49767269 × 327686000 - 1029 + \frac{1101}{32}

= 16308037309534000 - 1029 + \frac{1101}{32}

= 16308037309532972 + 34\frac{13}{32}

= 16308037309533006\frac{13}{32}

8 0
3 years ago
What is the equation of the line that passes through the point (–2,7) and has a slope of zero?
scZoUnD [109]

Answer:

y = 7

Step-by-step explanation:

Given:

x1 = -2

y1 = 7

slope (m) = 0

y - y1 = m ( x - x1 )

y - 7 = 0 ( x - (-2) )

y - 7 = 0 ( x + 2 )

y - 7 = 0

y = 7

4 0
2 years ago
A hair salon charges a fixed rate of $25.00 for a haircut and an additional $15 for any other services. Write a function to mode
goblinko [34]
25+15•3= 70 dollars she spent on the hair salon..... dang lotsa money
3 0
3 years ago
Read 2 more answers
a company is expanding its building area from 17,500 square feet to 21,175 square feet. what is the percentage increase of the a
NikAS [45]

Let's make an equation.

19,000x=24,320

This equation shows the percentage increase, which is x. Once we have x, we need to subtract 1 from it since in the equation the 1 shows that it's increeasing. All we need to do is divide both sides by 19,000.

24,320÷19,000

1,28-1=0.28; we need to multiply by 100 to find the increase.

0.28×100=28

So, the percentage increase is 28%.

3 0
3 years ago
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