MATHEMATICS HIGH SCHOOL

AA, BBB, and CCC are collinear, and BBB is between AAA and CCC. The ratio of ABABA, B to BCBCB, C is 1:21:21, colon, 2. If AAA is at (7,-1)(7,−1)left parenthesis, 7, comma, minus, 1, right parenthesis and BBB is at (2,1)(2,1)left parenthesis, 2, comma, 1, right parenthesis, what are the coordinates of point CCC?

Answers

Answer 1

Answer:

Answer:

The coordinates of point C are (-8,5).

Step-by-step explanation:

It is given that A, B and C collinear and B is between A and C.

The ratio of AB to BC is 1:2. It means Point divided the line segments AC in 1:2.

Section formula:

$((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n))$

The given points are A(7,-1) and B(2,1).

Let the coordinates of C are (a,b).

Using section formula the coordinates of B are

$B=(((1)(a)+(2)(7))/(1+2),((1)(b)+(2)(-1))/(1+2))$

$B=((a+14)/(3),(b-2)/(3))$

We know that point B(2,1).

$(2,1)=((a+14)/(3),(b-2)/(3))$

On comparing both sides we get

$2=(a+14)/(3)$

$6=a+14$

$6-14=a$

$-8=a$

The value of a is -8.

$1=(b-2)/(3)$

$3=b-2$

$3+2=b$

$5=b$

The value of b is 5.

Therefore, the coordinates of point C are (-8,5).

Answer 2

Answer:

The coordinates of the pointC such that pointsA and B are (7, -1) and (2, 1) and the ratioAB to BC is 1 : 2 is (-8, 5).

How to determine the location of a point within a line segment

According to the Euclidean geometry, a line is formed by two points on a plane and three points are collinear if all the three points go through a single line.

By definitions of vector and ratio we derive an expression to determine the coordinates of the point B:

$\overrightarrow{AB} = (1)/(1+2)\cdot \overrightarrow{AC}$

$\vec B - \vec A = (1)/(3)\cdot \vec C -(1)/(3)\cdot \vec A$

$(1)/(3)\cdot \vec C = \vec B - (2)/(3)\cdot \vec A$

$\vec C = 3 \cdot \vec B - 2\cdot \vec A$

If we know that A(x,y) = (7, -1) and B(x,y) = (2, 1), then the coordinates of point C is:

C(x, y) = 3 · (2, 1) - 2 · (7, -1)

C(x, y) = (6, 3) + (- 14, 2)

C(x,y) = (- 8, 5)

The coordinates of the pointC such that pointsA and B are (7, -1) and (2, 1) and the ratioAB to BC is 1 : 2 is (-8, 5).

Remark

The statement is poorly formatted and reports mistakes. Correct form is shown below:

A, B and C are collinear and B is between A and C. The ratio of AB to BC is 1 : 2. If A is A(x, y) = (7, -1) and B(x, y) = (2, 1), what are the coordinates of point C?

To learn more on line segments, we kindly invite to check this verified question: brainly.com/question/25727583

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Answers

Final answer:

Using the quadratic equation h = -16t² + 264 which represents the object's height after time, we find that it will take 4 seconds for the object to reach 8 feet above the valley floor.

Explanation:

In this case, you're asked to find out how much time it takes for an object dropped from an observation deck to drop to a point 8 feet above the valley floor. The height h, in feet, after time t, in seconds, is represented by the quadratic equation h = -16t² + 264. Set the equation equal to desired height, which is 8 feet in this case. So, you have -16t² + 264 = 8. Rearranging, you get -16t² = 8 - 264, or -16t² = -256. Divide by -16 yields, t² = 16. The principal square root of 16 is t = 4.

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HELP ASAP PLEASE I NEED HELP

Answers

Answer:

Step-by-step explanation:

I think it is I'm not sure but I hope it is

Within the metric system all units are based on the numbera. 1.
b. 100.
c. 10.
d. 1000.

Answers

Answer:

The answer is the option C $10$

Step-by-step explanation:

we know that

The metric system is a system of measuring based on the meter, kilogram and second (MKS). Is based on the powers of the number $10$

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If f(x)=3x+10x and g(x)= 2x-4, find (f+g)(x)

Answers

Answer:

=3^x +12x -4

Step-by-step explanation:

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g(x)= 2x-4,

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Combine like terms

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If the population of a country increases at a rate of 1.5% annually, and its current population is 430,000, how many years will it take for the population to triple?

Answers

Answer:

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Step-by-step explanation:

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