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
Vadim26 [7]
3 years ago
14

Given points $A(2,3)$, $B(-1,4)$, and $C(-2,-2)$, determine point $D$ so that the slope from $A$ to $B$ equals the slope from $C

$ to $D$, and the slope from $A$ to $D$ equals the slope from $B$ to $C$.
Mathematics
2 answers:
miss Akunina [59]3 years ago
7 0

Answer:

D is approximately (-2, -1)

Step-by-step explanation:

{ \tt{slope \:AB = slope \: CD }} \\  \\ { \tt{ \frac{(4 - 3)}{( - 1 - 2)}  =  \frac{(y - ( - 2))}{(x - ( - 2))} }} \\  \\ { \tt{ \frac{1}{ - 3} =  \frac{y + 2}{x + 2}  }} \\  \\ { \tt{x + 2 =  - 3y - 6}} \\ { \underline{ \tt{ \green{ \:  \: 3y + x =  - 8 \:  \: }}}}

{ \tt{slope \: AD= slope \:  BC}} \\ \\  { \tt{ \frac{y - 3}{x - 2}  =  \frac{ - 2 - 4}{ - 2 - 1} }} \\  \\ { \tt{ \frac{y - 3}{x - 2} =  \frac{6}{3}  }} \\  \\ { \tt{ \frac{y - 3}{x - 2}  = 2}} \\  \\ { \tt{y - 3 = 2(x - 2)}} \\  { \tt{y - 3 = 2x - 4}} \\ { \underline{ \tt{ \blue{ \:  \: y - 2x =  - 1 \:  \: }}}}

Solve the green equation and blue equation simultaneously:

{ \boxed{ \tt{ \red{ \: y \approx - 2 \:  \: }}and \:  \: { \red{x \approx - 1}}}}

gayaneshka [121]3 years ago
4 0

Let the co-ordinates of D be (a,b)

  • Slope of AB =Slope of CD

\\ \tt\hookrightarrow \dfrac{4-3}{-1-2}=\dfrac{b+2}{a+2}

\\ \tt\hookrightarrow \dfrac{-1}{2}=\dfrac{b+2}{a+2}

\\ \tt\hookrightarrow -a-2=2b+4

\\ \tt\hookrightarrow a+2b+6=0\dots(1)

  • Slope of AD=Slope of BC

\\ \tt\hookrightarrow \dfrac{b-3}{a-2}=\dfrac{-2-4}{-2+1}

\\ \tt\hookrightarrow \dfrac{b-3}{a-2}=6

\\ \tt\hookrightarrow 6a-12=b-3

\\ \tt\hookrightarrow 6a-b-9=0\dots(2)

Multiplying 2 with eq(2)

\\ \tt\hookrightarrow 12a-2b-18=0\dots(3)

  • Add eq(1) and (3)

\\ \tt\hookrightarrow 13a-12=0

\\ \tt\hookrightarrow a=12/13=0.9\to 1

  • Put in eq(1)

\\ \tt\hookrightarrow 12/13+2b+6=0

\\ \tt\hookrightarrow 90/13=-2b

\\ \tt\hookrightarrow b=-90/26=-3 4\to 3

You might be interested in
Please help if possible? :)
vova2212 [387]

Answer:

i think it 77 hope this helps

3 0
3 years ago
Read 2 more answers
Help!!!! What is the answer??????
ANTONII [103]

Answer:I think is A

Step-by-step explanation:

5 0
4 years ago
please use a peice of paper to write down your work and take a picture of it and put it here, I need to show my work there is 2
mihalych1998 [28]

The answer to question 1 is n=-17, and the answer to question 2 is y=-5.8 (<u>could also be seen as -29/8</u>)

Work is shown in the pictures below

4 0
3 years ago
8 (3x-y)<br> what is the answer
lesantik [10]

Answer:

24x-8y

Step-by-step explanation:

8 times 3x is 24x and 8 times y is 8y

8 0
3 years ago
Read 2 more answers
ANSWER ASAP PLS Eve knits scarves for her online store. This week she has already knitted 9 scarves. There are 2 days left in th
JulsSmile [24]

Answer:

4.

Step-by-step explanation:

Since Eve has already knitted nine scarves we just need to add of few more. Our equation is this: 9 + _ + _ = ?

If you do 9 + 4 + 4, you get 17. Therefor, Eve must knit four scarves per day to meet her goal.

5 0
4 years ago
Read 2 more answers
Other questions:
  • A test is worth 75 points. Multiple-choice questions are worth 2 points and
    13·1 answer
  • Factor t^2 - 4t + 4
    6·1 answer
  • Pls say the answers<br> i need this for my class activity
    9·1 answer
  • Please answer this correctly
    13·1 answer
  • Olivia bought snacks for her team's practice. She bought a bag of popcorn for $3.39
    6·1 answer
  • 7^2 + 4^3 ÷ 2^5<br> Lol please help
    9·2 answers
  • Please help me or no pizza
    15·2 answers
  • What is three more than the sum of (3,3)
    11·2 answers
  • Which is a factor of 144 − 49x2? 12 - 7x2 72 – 7x2 12 – 7x 72 7x.
    12·1 answer
  • What exponential expression is equal to 2^-5 . 2^8
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!