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RideAnS [48]
3 years ago
5

Point A is located at (3,6) and point B is located at (10, -2) What are the coordinates of the point that partitions the directe

d line segment AB in a 1:3 ratio?​
Mathematics
1 answer:
aliya0001 [1]3 years ago
6 0

Answer:

The coordinates of point P is (\frac{19}{4} ,4)

Step-by-step explanation:

Here, the coordinates of the point A and B are given as:

A (3,6) and B(10,-2)

Let us assume the point P (a,b) divides the line segment AB in ratio 1:3.

Now, by SECTION FORMULA:

The coordinate of the point (a,b) which divides the line segment with points (x1,y1) and (x2,y2) in ratio m1 : m2 is given as:

(a,b) = (\frac{m_2x_1 + m_1x_2}{m_1+m_2}, \frac{m_2y_1 + m_1y_2}{m_1+m_2})

Now, here putting the values of the points A and B as (3,6) and (10,-2) adn ratio m1 : m2 as 1:3, we get:

(a,b) = (\frac{3(3) + 1(10)}{1+3}, \frac{3(6) + 1(-2)}{1+3})\\\implies (a,b)= (\frac{9+10}{4} , \frac{18-2}{4})  =(\frac{19}{4} ,\frac{16}{4} )\\\implies (a,b) = (\frac{19}{4} ,4 )

Hence, the coordinates of point P is (\frac{19}{4} ,4)

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Answer:

Given radius (R) = 13

Diameter =  2R =  26

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=  81.681408993335

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Step-by-step explanation:

While a circle, symbolically, represents many different things to many different groups of people including concepts such as eternity, timelessness, and totality, a circle by definition is a simple closed shape. It is a set of all points in a plane that are equidistant from a given point, called the center. It can also be defined as a curve traced by a point where the distance from a given point remains constant as the point moves. The distance between any point of a circle and the center of a circle is called its radius, while the diameter of a circle is defined as the largest distance between any two points on a circle. Essentially, the diameter is twice the radius, as the largest distance between two points on a circle has to be a line segment through the center of a circle. The circumference of a circle can be defined as the distance around the circle, or the length of a circuit along the circle. All of these values are related through the mathematical constant π, or pi, which is the ratio of a circle's circumference to its diameter, and is approximately 3.14159. π is an irrational number meaning that it cannot be expressed exactly as a fraction (though it is often approximated as 22/7) and its decimal representation never ends or has a permanent repeating pattern. It is also a transcendental number, meaning that it is not the root of any non-zero, polynomial that has rational coefficients. Interestingly, the proof by Ferdinand von Lindemann in 1880 that π is transcendental finally put an end to the millennia-old quest that began with ancient geometers of "squaring the circle." This involved attempting to construct a square with the same area as a given circle within a finite number of steps, only using a compass and straightedge. While it is now known that this is impossible, and imagining the ardent efforts of flustered ancient geometers attempting the impossible by candlelight might evoke a ludicrous image, it is important to remember that it is thanks to people like these that so many mathematical concepts are well defined today.

Circle Formulas

D = 2R

C = 2πR

A = πR2

where:

R: Radius

D: Diameter

C: Circumference

A: Area

π: 3.14159

6 0
2 years ago
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