A triangle has vertices at (1,10), (-5,2), and (7,2). What is its orthocenter. Show your work.

Answers

Answer 1

Answer:

Question: What is the orthocenter of a triangle with the vertices (-1,2) (5,2) and (2,1)?

The coordinates of point A are (-1,2), point B are (5,2), and point C are (2,1).

The orthocent is the intersection of the three altitudes. An altitude goes from a vertex and is perpendicular to the line containing the opposite side.

In the coordinate plane the equations of the altitudes can be found and then a system of equations can be solved.

Altitude 1. From point C perpendicular to the line containing side AB.

Slope of line AB is 0 (horizontal line), a vertical line is perpendicular to a horizontal line. Thus, the equation of altitude 1 is  x=2 .

Altitude 2. From point B perpendicular to the line containing side AC.

Slope of line AC is  −13 , the slope of a line perpendicular to line AC is 3. The equation of altitude 2 is  y=3x−13  

Altitude 3. From point A perpendicular to the line containing side BC.

Slope of line BC is  13 , the slope of a line perpendicular to line BC is  −3 . The equation of altitude 3 is  y=−3x−1  

The orthocenter is the point where all three altitudes intersect.

x=2  

y=3x−13  

y=−3x−1  

Use substitution to solve the first two equations  y=3(2)−13=−7  

The orthocenter is the point  (2,−7)  

we did not need the third equation, but we can use it as a check, plug the coordinates into the third equation:

−7=−3(2)−1  

−7=−6−1  

−7=−7  it works.


Related Questions

What is the value of f(x) = 2 • 2x for f(–2)?

Answers

Answer:

0.0625

Step-by-step explanation:

because the other answer is wrong.

(and bad) :)

Solve the equation x2 + 4x − 11 = 0 by completing the square. Fill in the values of a and b to complete the solutions.

Answers

Answer:

x = - 2 -[tex]\sqrt{15\\[/tex]

x = - 2 + [tex]\sqrt{15[/tex]

Step-by-step explanation:

The given equation needs to be solved by completing the squares.

The required values are -2+√15, -2-√15

Completing the squares

The given equation is [tex]x^2+4x-11=0[/tex]

The general form of a quadratic equaiton is [tex]ax^2+bx+c=0[/tex]

Comparing with the given equation we have

a = 1

b = 4

c = -11

Rearranging the equation

[tex]x^2+4x=11[/tex]

Finding (b/2)²

[tex](\dfrac{4}{2})^2=4[/tex]

Adding to both sides of the equation

[tex]x^2+4x+4=11+4\\\Rightarrow (x+2)^2=15\\\Rightarrow x+2=\pm\sqrt{15}\\\Rightarrow x=-2+\sqrt{15},-2-\sqrt{15}[/tex]

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PLS HELP !!!!!!!!!!!!!!!!!!

pls show ur work

Answers

Answer:

The skier has a faster rate of speed.

Snowboarder: 15m/s

skier: 18 m/s

Step-by-step explanation:

plzzz help me with this math im so confused!!

Answers

Answer:

I have made it in above picture

Answer:

2 A.)

1) 3-4x+8x^2-6+2x-5x^2

2) 8x^2-5x^2-4x+2x+3-6

3) 3x^2-2x-3

B.) 3x-5-7x^2+2+6x^2+5x

Step-by-step explanation:

please mark brainiest

please give 5 stars

thank you

PLEASE ANSWER FAST AS POSSIBLE I HAVE 40 LESSONS DUE BY 12 PM :(

Answers

Try B, hope that helps :)

Answer: B

Step-by-step explanation: Skeletons serve as a scaffold which supports organs, anchors muscles, and protect organs such as, the brain, lung, heart, and spinal cord.

Kiran has 27 nickels and quarters in his pocket, worth a total of $2.75.

B. How many nickels and quarters are in Kiran's pocket? Show your reasoning.

Answers

Answer:

1.35 about 6 quarters

Step-by-step explanation:

2.75-1.35=1.40

1.40/0.25=about 6

Answer:

there will be 20 nickels and 7 quarters

Consider the rectangular prism.
8 cm
14 cm
6 cm
How many cubes with side lengths of a cm can fit inside the rectangular prism?
0672 cubes
1, 344 cubes
2,688 cubes
0 5,376 cubes

Answers

Answer:

672 cubes because 8×6×14 equals 672 I hope it helps

To rent a party room, customers
are charged an amount equal to the number
of hours they rent plus a $60 cleaning fee.
What is the cost of a 3-hour rental?

WILL MARK BRANLIEST !!

Answers

Answer:

78

Step-by-step explanation:

im not sure but i think is 78

60+18=78

sorry

HELP PLEAAAASEEE LOLOLOL

1.Find the slope of the line graphed below.

A. 1/2
B. 2
C. -1/2
D. -2

Answers

THE ANSWER WILL BE c

I REALLY NEED HELP! PLEASE HELP ME!!

A burger cost $10 while a hot dog cost $6. What is the ratio of the cost of burger to hot dog?

Answers

Answer:

5:3

Step-by-step explanation:

a burger cost 10 and a hot dog cost 6 so the ratio is literally 10:6 if u want a simplified answer divide both numbers by 2

5:3

Answer: 3:5

Step-by-step explanation:

100000x5000000+997890-8

Answers

Answer:

500,000,997,882

Step-by-step explanation:

fun fact: the average tree frog weighs 0.8 ounces

Answer:

500000997882

Step-by-step explanation:100000 5000000 times is 500000997882.

Loren made a scale map of his football field to prepare for the big game. The length
of the football field on his map was 3 in. In reality the football field is 100 yards long.
What is the scale factor?

Answers

Answer:

1200

Step-by-step explanation:

brainliest please :D

Pls someone answer these 2 questions ill mark you as brainliest pls pls asap

Answers

I’ve stitched my work...
Hope this helps!

Pls help me with this answer

Answers

Answer:

3.3x10^4

Step-by-step explanation:

2. The two equations y = (x + 2)(x + 3) and y = x? + 5x + 6 are equivalent.

a. Which equation helps find the x-intercepts most efficiently?

b. Which equation helps find the y-intercept most efficiently?

Answers

Answer:

it b

Step-by-step explanation:

a) y = (x + 2)(x + 3)  helps find the x-intercepts most efficiently.

b) y=   [tex]x^{2} +5x+6[/tex] helps find the y-intercept most efficiently

What is intercepts?

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

Given that:

a) y= (x+2)(x+3)

i.e., x+2= 0 , x+3 = 0

    x= -2 , x= -3

and, y =  [tex]x^{2} +5x+6[/tex]

           = (x+2)(x+3)

  x= -2 and y= -3

y = (x + 2)(x + 3) helps to find the x-intercepts most efficiently

Now,

b) y=(x+2)(x+3)

     x =0 , y = 2 x 3 =6

y=   [tex]x^{2} +5x+6[/tex]

y= 0 +05 x 0 + 6

y= 6

So, for y-intercept use  y=   [tex]x^{2} +5x+6[/tex]

   

Learn more about intercepts here:

https://brainly.com/question/14180189

#SPJ2

pls answer it now!!

argatogozaimasu!!​

Answers

Answer:

850 and 23

Step-by-step explanation:

Can someone please help me

Answers

Answer:

radius = 10

(x-5)² + (y-11)² = 100

Step-by-step explanation:

The circumference is given, we get r = 20π/2π = 10

∴Equation of circle is (x-5)² + (y-11)² = 100

Answer:

hiii

Step-by-step explanation:

A polynomial p has zeros when x = 5,2 = -1, and 2
1
4
What could be the equation of p?

Answers

Answer:

apolynomial p has zeros

Answer:

p(x)=(x-5)(x+1)(4x+1)

When n = 3, which of the expressions below will be greater than 50? Select all that apply. A) (8n2÷9)⋅7 B) 2n2⋅3 –4n C) 4n2–6n+12 D) 7n+(n⋅8)

Answers

Answer:

A

Step-by-step explanation:

a)

[tex](8(3)^{2} / 9) * 7[/tex]

8(9) / 9 = 8 x 7 = 56

b)

[tex]2(3)^{2} * 3 - 4(3)[/tex]

2(9) * 3 - 12

18 * 3 = 54 - 12 = 42

c)

[tex]4(3)^{2} - 6(3) + 12[/tex]

4(9) - 18 + 12

36 - 18 = 18 + 12 = 30

d)

[tex]7(3) + (3 * 8)[/tex]

21 + 24 = 45

Someone help me ASAP !

Answers

Answer:

31

Step-by-step explanation:

There are 40 students in The class. Nine of those students are girls. What is the number of boys in the class ?

Answers

Answer:

31 students

Step-by-step explanation:

Han wrote a proof that triangle BCD is congruent to triangle DAB. Han's proof is incomplete. Which step is missing some information? DC∥AB
Step 1: Line AB is parallel to line DC and cut by transversal DB. So angles CDB and ABD are alternate interior angles and must be congruent.
Step 2: Side DB is congruent to side BD because they're the same segment.
Step 3: Angle A is congruent to angle C because they're both right angles.
Step 4: By the Angle-Side-Angle Triangle Congruence Theorem, triangle BCD is congruent to triangle DAB .
and WHY?

Answers

Answer:

The answer is below

Step-by-step explanation:

From the image, we can see that DC is parallel to AB.

Step 1:

Alternate interior angles are angles formed at the inner corners of intersection on opposite sides of transversal when two parallel lines are intersected by a transversal.

Since Line AB is parallel to line DC and cut by transversal DB. So angles CDB and ABD are alternate interior angles and must be congruent.

Step 2:

DB ≅ BD (reflexive property of congruence)

Step 3:

∠A = ∠C = 90° (right angles, given). But to prove that both triangles are congruent, the correct step 3 is:

Since, ∠A = ∠C = 90° and angles CDB and ABD are congruent. This means that the third angles in the both triangles are also congruent. Hence, angle ADB and CBD are must be congruent.

Step 4:

BD = DB, angles CDB and ABD  are congruent, angle ADB and CBD are congruent.

Therefore,  By the Angle-Side-Angle Triangle Congruence Theorem, triangle BCD is congruent to triangle DAB .

Expand and simplify (y+3)-(y-2)

Answers

(y + 3) - (y - 2)

= y + 3 - y + 2

= y - y + 3 + 2

= 5

Answer:

5

Step-by-step explanation:

Given

(y + 3) - (y - 2) ← distribute parenthesis

= y + 3 - y + 2 ← collect like terms

= 5

PLZZZZZZ HEEEEEEEEELLLLLPPPPP
(will mark brainliest for correct answers)

Answers

Answer:

y=4

Step-by-step explanation:

3(9) +4y= 43

27+4y=43

4y=16

y=4

It says shade 3/4 of this figure

Answers

3/4=?/8, as there are eight rectangles.
3*2/4*2=6/8

Answer:

I think you shade in 6 of the rectangles

help me please with my geometry

Answers

Answer: 47.86

Step-by-step explanation:

tan x =42/38

tan x= 1.105

x= 47.86

If these four countries trade only with each other, what is the difference between the highest balance of trade and the lowest

balance of trade within this group?

a €4,378,000,000

€2,797,000,000

€1,928,000,000

d €738,000,000

Answers

Answer:

€4,378,000,000

Step-by-step explanation: just took the test :)

Answer:

A

Step-by-step explanation:

Took the test

The number of people using an older version of a spreadsheet program decreases at a rate that is proportional at any time to the number of people still using the version at that time.

There were 10,000 people using the older version of the spreadsheet program when the new version first came out. The number of people still using the older version decreases by 20%, percent every 6 months.

Answers

Answer:

5842 people after 2 months

Step-by-step explanation:

Given

Initial Value: [tex]a =10000[/tex]

Rate: [tex]r = 20\%[/tex] every 6 months

Required

Number of people using it after 2 months

The function follows an exponential model.

So, we need to first write out the function.

If Rate: [tex]r = 20\%[/tex] every 6 months

Then

Rate: [tex]r = 40\%[/tex] after 1 year

[tex]r = 0.04[/tex]

The function is represented as:

[tex]y = ar^x[/tex]

So:

[tex]y = 10000 * 0.04^t[/tex]

For 2 months, we have:

[tex]t = 2\ months[/tex]

Convert to years

[tex]t = \frac{2}{12}[/tex]

[tex]t = 0.167[/tex]

[tex]y = 10000 * 0.04^t[/tex]

[tex]y = 10000 * 0.04^{0.167}[/tex]

[tex]y = 5842[/tex]

HELP ME PLZ !!!!!!!!

Answers

Answer:

LM=JM

Step-by-step explanation:

If Jk=Lk Maybe that K was not 90 This means that the triangles are not congruent if it was K = 90 maybe Jk ≠ Lk and that means the two triangles are not congruentif LM = GM و MK = MK It means that the two triangles are congruent

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Find the area of the parallelogram. A parallelogram has a lower side measuring 24 centimeters and a right side measuring 9 centimeters. A dashed vertical segment with endpoints on the upper and lower sides is 8 centimeters and meets the lower left vertex at a right angle.

Answers

Answer:

[tex]Area = 192cm^2[/tex]

Step-by-step explanation:

The given information can be interpreted as:

[tex]Base = 24cm[/tex] --- lower side

[tex]Slant\ Height = 9cm[/tex] --- right side

[tex]Height = 8cm[/tex] --- dashed line

Required

Determine the area

The area of parallelogram is:

[tex]Area = Base * Height[/tex]

[tex]Area = 24cm * 8cm[/tex]

[tex]Area = 192cm^2[/tex]

Answer:

she like

Step-by-step explanation:

faygo u gettin bigger

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