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
frutty [35]
3 years ago
11

A (0, 2) and B (6,6) are points on the straight line ABCD.

Mathematics
2 answers:
elena-14-01-66 [18.8K]3 years ago
8 0

Answer:

(18, 14)

Step-by-step explanation:

We know that C and D lie on the line AB and BC = CD = AB. Then we need to use the distance formula and equation of the line AB to find the other two coordinates.

The distance formula states that the distance between two points (x_1,y_1) and (x_2,y_2), the distance is denoted by: \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}. Let's find the distance between A and B:

d = \sqrt{(6-0)^2+(6-2)^2}=\sqrt{6^2+4^2} =\sqrt{36+16} =\sqrt{52} =2\sqrt{13}

Now say the coordinates of D are (a, b). Then the distance between D and B will be twice of 2√13, which is 4√13:

4√13 = \sqrt{(6-a)^2+(6-b)^2}

Square both sides:

208 = (6 - a)² + (6 - b)²

Let's also find the equation of the line AB. The y-intercept we know is 2, so in y = mx + b, b = 2. The slope is (6 - 2) / (6 - 0) = 4/6 = 2/3. So the equation of the line is: y = (2/3)x + 2. Since (a, b) lines on this line, we can put in a for x and b for y: b = (2/3)a + 2. Substitute this expression in for b in the previous equation:

208 = (6 - a)² + (6 - b)²

208 = (6 - a)² + (6 - (2/3a + 2))² = (6 - a)² + (-2/3a + 4)²

208 = a² - 12a + 36 + 4/9a² - 16/3a + 16 = 13/9a² - 52/3a + 52

0 = 13/9a² - 52/3a - 156

13a² - 156a - 1404 = 0

a² - 12a - 108 = 0

(a + 6)(a - 18) = 0

a = -6 or a = 18

We know a can't be negative so a = 18. Plug this back in to find b:

b = 2/3a + 2 = (2/3) * 18 + 2 = 12 + 2 = 14

So point D has coordinates (18, 14).

TiliK225 [7]3 years ago
6 0

Answer:

D: (18,14)

Step-by-step explanation:

AB: < 6-0 , 6-2 >

AB: < 6 , 4 >

OD = OB + 2(AB)

OD = < 6 , 6 > + 2< 6 , 4 >

OD = < 6+12 , 6+8 >

OD = < 18 , 14 >

D: (18,14)

You might be interested in
Write a slope- intercept equation for a line with given characters m=-4/5, passes through (-4,-5)
aleksandr82 [10.1K]

\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-5})~\hspace{10em} \stackrel{slope}{m}\implies -\cfrac{4}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{-\cfrac{4}{5}}[x-\stackrel{x_1}{(-4)}]\implies y+5=-\cfrac{4}{5}(x+4) \\\\\\ y+5=-\cfrac{4}{5}x-\cfrac{16}{5}\implies y=-\cfrac{4}{5}x-\cfrac{16}{5}-5\implies y=-\cfrac{4}{5}x-\cfrac{41}{5}

6 0
3 years ago
Finally, the arena decides to offer advertising space on the jerseys of the arena’s own amateur volley ball team. The arena want
bagirrra123 [75]

Answer: 7/50

14%

1/30

Step-by-step explanation:0.14 to fraction =0.14/100=14/100=7/50

0.14 to %= 0.14 ×100=14%

Total number of balls=6

Blue balls=2

Golden balls=2

Green balls=2

Probability of picking the first ball=1/6

Probability of picking the second ball= 1/5

P(winning wit 2 golden balls)=1/6×1/5=1/30

6 0
3 years ago
Using tour answer from base e, ale
Natasha2012 [34]

That’s all correct thanks

5 0
3 years ago
Can someone explain to me how to do this
rusak2 [61]

rank | 1st | 2nd |TOTAL
------|-----+-------|----------
a     | 6   +    9   |  =15
b     | 7   +   3    | =16
c     | 9   +   7    | =23
d     | 6   +   7    | =22
e     | 8   +  1     | =?


If you add the 1st in line a (6) and you add it to the 1st in line b (7) + the 2nd in line b (3) you get 16. Repeat the same logic/pattern to all c,d..
This is the pattern to all this puzzle;

So the before last term is :  9+6+7 = 22
and the last term : 6+8+1 = 15


7 0
3 years ago
Given the function f(x) = 3|x – 2| + 6, for what values of x is f(x) = 18?
Radda [10]
C
..............................
5 0
3 years ago
Read 2 more answers
Other questions:
  • 6x+8y=30
    14·1 answer
  • A vehicle has travelled 90 miles at 40mph
    5·1 answer
  • Which is greater 3/7 3/6 3/5
    14·2 answers
  • Suppose you can climb to the top of the pyramid arena in Memphis Tennessee which path would be shorter climbing a lateral Edge o
    6·1 answer
  • Which type of graph uses the length of bars to show how many data points are in interview
    6·1 answer
  • If the measure of an exterior angle drawn at vertex M
    9·2 answers
  • What is the factored form of this expression?
    7·1 answer
  • What is 4/5 = 12/blank | Equivalent Fractions
    15·2 answers
  • A linear function contains the following points.
    6·1 answer
  • Can you pls help me with this question thank you
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!