The vertices of a triangle are A(-2, 1), B(2, 2) and C(6, - 2).
Find the equation of the altitude of AD drawn from A to BC.​

Answers

Answer 1

Answer:

The equation of altitude AD drawn from A to BC will be:

[tex]y=x+3[/tex]

Step-by-step explanation:

Let m₁ and m₂ be the slope of line AD and BC respectively.

Now, AD⊥BC

​∴ m₁ × m₂ = -1

be the slope of line AD and BC respectively.

⇒ m₁ = -1/m₂    → (A)

Finding the slope of BC using points

B(2, 2)

C(6, - 2)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(2,\:2\right),\:\left(x_2,\:y_2\right)=\left(6,\:-2\right)[/tex]

[tex]m_{2} =\frac{-2-2}{6-2}[/tex]

[tex]m_{2} =-1[/tex]

On substituting the value of m₂ in equation (A)

m₁ = -1/m₂

    = -1/(-1)

    = 1

We know that the point-slope form of the line equation is

[tex]y-y_1=m\left(x-x_1\right)[/tex]

∴ Equation of altitude AD passing through A(-2, 1) with slope 1 will be

[tex]y-1=1\cdot \left(x-\left(-2\right)\right)[/tex]

[tex]y-1=x+2[/tex]

[tex]y=x+3[/tex]

Therefore, the equation of altitude AD drawn from A to BC will be:

[tex]y=x+3[/tex]


Related Questions

Graph the equation
y-3=-3/2(x+4)

Answers

Answer: x = (-2,0) y = (0,-3) slope is -3/2

Step-by-step explanation: graph the line  by  using the slope and y intercept

The graph for the points (0, -3) and (2, -6) is plotted on the graph below.

The given equation is y-3= -3/2(x+4).

What is the graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

Graph the line using the slope and y-intercept, or two points.

Slope: -3/2

y-intercept: (0, -3)

Plot the points (0, -3) and (2, -6) on the graph

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (−2,0)

y-intercept(s): (0,−3)

Therefore, the graph for the points (0, -3) and (2, -6) is plotted on the graph below.

To learn more about the graph visit:

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Two triangles have the same height. The base of one
triangle is twice that of the other. Find the difference in
their areas.​

Answers

[tex]\huge\underline{\overline{\mid{\bold{\red{ANSWER}}\mid}}}[/tex]

They both have same height,

let the height of both triangles be = x

let the base one triangle = y

then the base of another trainlgle = 2y

Area of triangle = 1/2 X B X H

Area of Triangle 1

[tex] \frac{1}{2} \times y \times x \\ = > \frac{xy}{2} [/tex]

Area of Triangle 2

[tex] \frac{1}{2} \times 2y \times x \\ = > \frac{2xy}{2} \\ = > xy[/tex]

Difference in the area =

[tex]xy - \frac{xy}{2} \\ = > \frac{2xy - xy}{2} \\ = > \frac{xy}{2} [/tex]

Hence Area of Triangle 1 is half the area of Triangle 2

Difference of 1/2 area.

Answer:

[tex]\huge\underline{\overline{\mid{\bold{\red{ANSWER}}\mid}}}∣ANSWER∣

They both have same height,

let the height of both triangles be = x

let the base one triangle = y

then the base of another trainlgle = 2y

Area of triangle = 1/2 X B X H

Area of Triangle 1

\begin{gathered} \frac{1}{2} \times y \times x \\ = > \frac{xy}{2} \end{gathered}21×y×x=>2xy

Area of Triangle 2

\begin{gathered} \frac{1}{2} \times 2y \times x \\ = > \frac{2xy}{2} \\ = > xy\end{gathered}21×2y×x=>22xy=>xy

Difference in the area =

\begin{gathered}xy - \frac{xy}{2} \\ = > \frac{2xy - xy}{2} \\ = > \frac{xy}{2} \end{gathered}xy−2xy=>22xy−xy=>2xy

Hence Area of Triangle 1 is half the area of Triangle 2

Difference of 1/2 area.

[/tex]

Step-by-step explanation:

side it

siso,;-):-(

A total of 2000 people attended a benefit concert was held to raise money for a children foundation. Student ticket cost $2 and an adult ticket cost $3. If the organizer raises a total of $5050, how many students attended the concert?

Answers

Answer:

257 kids

Step-by-step explanation:

I need to find the slope for the question: 6y-14x=2

Answers

Answer:

Step-by-step explanation:


3. The product of two rational numbers is 15. If one of the numbers is - 10, find the other.​

Answers

Answer: -1.5

because one of the numbers is - 10 => the other is 15/-10 = -1.5

Step-by-step explanation:

Letf(x)=(x+2)2. Letg(x)=3(x+2)2. Which statement describes the graph of g(x) with respect to the graph of f(x)?

Answers

Answer:

I say two.

Step-by-step explanation:

Decrease £40 by 70%

plz answer and ill brainlist u!

Answers

Answer:

12

Step-by-step explanation:

Answer:

£12

Step-by-step explanation:

It's asking us to find the 30% of the 40 and to do this we multiply 40 by 30 then divide it by 100

40 × 30 ÷ 100 = 12

Find the measurement?

Answers

Answer:

HG = 28

Step-by-step explanation:

The midsegment MN is half the sum of the 2 parallel bases, that is

[tex]\frac{HG+JF}{2}[/tex] = MN , that is

[tex]\frac{HG+16}{2}[/tex] = 22 ( multiply both sides by 2 )

HG + 16 = 44 ( subtract 16 from both sides )

HG = 28

Alice needs twice as many yards of ribbon as Quincy. how many rolls of ribbon does Alice need? explain your answer i like your cut g

Answers

Twice the length of 322 yards is 644. If I divide by 15 I get 42 r14. Alice needs to buy 43 rolls of ribbon .

Answer: Twice the length of 322 yards is 644. If I divide by 15 I get 42 r14. Alice needs to buy 43 rolls of ribbon. I like your cut G !

Step-by-step explanation:

& represents 29 students in a class
B represents students who have a brother
S represents students who have a sister
В.
S
7
4
2x
x + 3
7+4+2x+x+3=29
a) One student from the class is chosen at random.
What is the probability that the student has a sister? 14+3x=29
3x=15
X=5
29-8=21​

Answers

Answer:

a) 14/ 29

b) 4/11

Step-by-step explanation:

x = 5

i can’t figure this one out

Answers

Answer:

H.

Step-by-step explanation:

the number of premiums sold in week 3 was 50

the number of premiums sold in week 2 was 25

25 times 2 is 50

PLEASE HELP
Alex wants to paint one side of his skateboard ramp with glow-in-the-dark paint, but he needs to know how much area he is painting. Calculate the area of the isosceles trapezoid.

140 ft2
160 ft2
180 ft2
200 ft2

Answers

Answer:

D.) 200ft²

Step-by-step explanation:

The formula for the area of a trapezoid:

[tex]A=\frac{1}{2} (b_{1}+b_{2})h[/tex]

where:

[tex]b_{1}[/tex] and [tex]b_{2}[/tex] are the basesh is the height

Insert the given values:

[tex]A=\frac{1}{2}(16+24)*10[/tex]

Simplify the equation using PEMDAS. Simplify parentheses:

[tex]A=\frac{1}{2}*40*10[/tex]

Simplify multiplication:

[tex]A=\frac{1}{2}* 400[/tex]

Simplify multiplication. Use the rule [tex]\frac{a}{b}*c=\frac{ac}{b}[/tex] :

[tex]A=\frac{1*400}{2}\\\\A=\frac{400}{2}[/tex]

Simplify division:

[tex]A=200[/tex]

The area is 200ft²

:Done

working on a song for someone I used to love
I'll go through all of the realities to find you
(If I need you)
Just so I can hold your hand...
Even if they think it's fake...
I want you to understand
that there's a certain miss
and a certain love
and a heartache in my chest
every time i hear your name
and im still lying in my bed
without you....

Answers

Answer:

wowww!! it's very sad and wonderfull

–1.0 ? |–4.4| Is it. Greater than. Less than or equal to

Answers

Answer:

Less Than

Step-by-step explanation:

Answer:

-1.0 is greater than -4.4

Explain in your own words why you would use division to change a smaller unit to a bigger one . What would happen if you multiplied instead ? TOPIC IS MEASUREMENT

Answers

Answer:

you would use division to change bigger units into smaller ones as a form of cancellation

how do i solve -3=-2x+1 by graphing?

Answers

Answer:

x = 2

Step-by-step explanation:

-3 = -2x + 1

minus 1 to the both sides

-3 -1 = -2x

-4 = -2x

divide both sides by -2

x = 2

PLEASE HELP!!!!! 2.) What is the perimeter of a polygon with vertices at (-3, 1), (5, 1), (-3, 4), (5, 4)? 30 points if you can help

Answers

Answer:

22 units.

Step-by-step explanation:

We want to find the perimeter of the polygon with vertices at: (-3, 1); (5, 1); (-3, 4); and (5, 4).

Let’s first plot the points and see what polygon we acquire. Please refer to the graph below.

As we can see, when plotting the points and connecting them, we get a rectangle.

So, we can use the perimeter formula for a rectangle, given by:

[tex]P=2(\ell+w)[/tex]

Where [tex]\ell[/tex] Is the length and [tex]w[/tex] is width.

Remember that the perimeter is simply the distance around the figure.

So, let’s find the length. We can do so by counting or by subtracting.

By counting, we can see that the length (longer side) is 8 units.

And by subtracting, we get the same length of |5-(-3)| or 8 units.

We use absolute value because distance is always positive.

Using the same process, we find the width to be 3 units.

Using subtract, we can see that this is indeed true as |1-4|=3.

So, we can now substitute the values into our formula:

[tex]P=2(8+3)[/tex]

Evaluate:

[tex]P=2(8+3)=2(11)=22\text{ units}[/tex]

So, the perimeter of the polygon is 22 units.

A sociologist polled a random sample of people and asked them their age and annual income. The two-way frequency table below shows the results. Annual income vs. age group Less than $50,000 At least $50,000 Total Ages 44 and under 148 68 216 Ages 45 and above 38 94 132 Total 186 162 348 Which of the following statements is true of those polled? Choose 1 answer: А A person with an annual income of less than $50,000 is more likely to be 45 years old or above. B A person in the 44 and under age group is more likely to to have an annual income of at least $50,000​

Answers

Answer:

C A person with an annual income of at least \$50{,}000$50,000dollar sign, 50, comma, 000 is more likely to be 454545 years old or above

A person in the 44 and under age group is more likely to have an annual income of at least $50,000​ is a correct statement.

We have given that,

A sociologist polled a random sample of people and asked them their age and annual income.

What is the annual income?

annual income is the amount of money you receive during the year into your bank account, before any deductions.

The two-way frequency table below shows the results.

Annual income vs. age group Less than $50,000 At least $50,000

Total Ages 44 and under 148 68 216 Ages 45 and above 38 94 132

Total 186 162 348

A person with an annual income of at least

[tex]=\$50000\\=$50,000dollar[/tex]

Therefore statement b is true.

A person in the 44 and under age group is more likely to have an annual income of at least $50,000​.

To learn more about the annual income visit:

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The gross domestic product (GDP) of France is about $2.00 × 10 12 12 , and the GDP of Tuvalu is about $4.00 × 10 7 7 . How many times larger is the GDP of France than the GDP of Tuvalu?

Answers

Answer:

France's GDP is 50 000 times larger than Tuvalu's GDP.

Step-by-step explanation:

Given: Gross Domestic Product (GDP) of France = $2.0 x [tex]10^{12}[/tex]

            Gross Domestic Product (GDP) of Tuvalu = $4.0 x [tex]10^{7}[/tex]

To determine the number of times in which the GDP of France is greater than that of Tuvalu, divide the GDP of France by the GDP of Tuvalu.

[tex]\frac{2.0*10^{12} }{4.0*10^{7} }[/tex] = [tex]\frac{2000000000000}{40000000}[/tex]

           = [tex]\frac{200000}{4}[/tex]

           = 50000

Therefore, France's GDP is 50 000 times larger than Tuvalu's GDP.

which equation repersent functions?

2x+3y=10
4x=16
2x-3=14
3y=18
14.6=2x​

Answers

Answer:

y= (-2/3)x+10/3  is a function

3y=18 is a function

Step-by-step explanations

in both cases for each input x there is exactly one output y

In (2x-3) +In (3x+4)

Answers

Answer: x=7

Step-by-step explanation: is that what you're looking for?

Parker owns a food truck that sells tacos and burritos. He sells each taco for $3.25 and each burrito for $7. Yesterday Parker made a total of $552 in revenue from all burrito and taco sales and there were twice as many burritos sold as there were tacos sold. Write a system of equations that could be used to determine the number of tacos sold and the number of burritos sold. Define the variables that you use to write the system.

Answers

Answer:

let t= the number of tacos sold

let b= the number of burritos sold

3.25t+7b=552

b=2t

Step-by-step explanation:

Since there were twice as many burrito sold as tacos sold, there were more burritos sold, so if we multiply by 2 the number of tacos sold, we will get the number of burritos sold, meaning b=2t.

The system of equation should be considered as the  3.25t+7b=552 and the value of b should be equivalent to 2t.

Calculation of the equation:

here we assume that

t= the number of tacos sold

And, b= the number of burritos sold

As per the situation, the equation be like

3.25t+7b=552

b=2t

So,

put b value in the first equation

3.25t + 14t = 552

t = 3.01

And, b = 1.51

Learn more about an equation here: https://brainly.com/question/24603753

y-2 = -3(x + 6), write the equation of the line in slope intercept form.

Answers

Answer:

y = -3x - 16

Step-by-step explanation:

Point-slope form: y - y1 = m(x - x1)

Given: y - 2 = -3(x + 6)

Slope-intercept form: y = mx + b

To write the equation in slope-intercept form, we need to know the slope(m) and the y-intercept(b). By looking at the given equation, we can see that the slope is -3. We are also given the value of one point: (-6, 2).

To find the y-intercept, input the given values of the slope and the point into the equation format and solve for b:

y = mx + b

2 = -3(-6) + b

2 = 18 + b

Subtract 18 from both sides of the equation to isolate b:

2 - 18 = 18 - 18 + b

-16 = b

The y-intercept is -16.

Now that we know the slope and the y-intercept, we can write the equation:

y = -3x - 16

1. The price of a ring is directly proportional to its weight. If 10grams ring worth is
$3000, what is the weight of a ring worth $9000?​

Answers

30g

your welcomeeeeeeeeeeeee

HAIIIIIII PLS HELPPPPPP
dis is confusing -_-
Miguel has $30. He spends $8.00 on a movie ticket, $3.85 for snacks and $1.00 for bus fare each way.

How much money does Miguel have left?
Miguel has_____dollars left

Answers

Answer:

$16.5

Step-by-step explanation:

$30-$8-$3.85-$1-$1 = $16.5

What is a question that could be used to collect categorical data??

Answers

Other examples of categorical data include questions about gender, ethnicity, type of business, job position in the company, etc. ... a question that can be answered by a yes or a no.

9/4 ÷ 3/8

HELP ME PLS​

Answers

Answer:

the answer is 6 u welcome

In RST, RS=15, RT=12, and ST=17. Which angle of RST has the smallest measure?

Answers

Answer:A

Step-by-step explanation: I took the test

plss show the work

6 − 4v = 3 − v

Answers

Answer: = 1

Step-by-step explanation: 6−4v=3−v

Step 1: Simplify both sides of the equation.

6−4v=3−v

6+−4v=3+−v

−4v+6=−v+3

Step 2: Add v to both sides.

−4v+6+v=−v+3+v

−3v+6=3

Step 3: Subtract 6 from both sides.

−3v+6−6=3−6

−3v=−3

Step 4: Divide both sides by -3.

−3v

−3

=

−3

−3

v=1

Answer:

v=1

Answer:

V=1

Step-by-step explanation:

6 - 4v = 3 - v

move the varible

6 - 4v + v = 3

collect like terms

-3v = 3 - 6

divide both sides by -3

V = 1

Is X +3 a factor of 2X squared minus 2X -12

Answers

Answer: No, x+3 is not a factor of 2x^2-2x-12

========================================================

Explanation:

Let p(x) = 2x^2 - 2x - 12

If we divide p(x) over (x-k), then the remainder is p(k). I'm using the remainder theorem. A special case of the remainder theorem is that if p(k) = 0, then x-k is a factor of p(x).

Compare x+3 = x-(-3) to x-k to find that k = -3.

Plug x = -3 into the function

p(x) = 2x^2 - 2x - 12

p(-3) = 2(-3)^2 - 2(-3) - 12

p(-3) = 12

We don't get 0 as a result so x+3 is not a factor of p(x) = 2x^2 - 2x - 12

----------------------------------------

Let's see what happens when we factor p(x)

2x^2 - 2x - 12

2(x^2 - x - 6)

2(x - 3)(x + 2)

The factors here are 2, x-3 and x+2

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