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2 years ago

el valor del punto px que divide con razon de 1/4 al segmento AB considerando los puntos A (3,1) y D(8,9)

Mathematics

1 answer:

vitfil [10]2 years ago

3 0

Answer:

(4, 13/5)

Step-by-step explanation:

Aquí, estamos encontrando el punto que divide el segmento en 1/4

supongamos que tenemos la proporción 1: 4 como a: b

Matemáticamente, el punto que divide el segmento será;

Coordenada x = (bx1 + ax2) / (a + b)

donde (x1, x2) = (3,8)

Al conectar estos valores, tenemos; (4 (3) + 1 (8) / (1+ 4) = (12 + 8) / 5 = 20/5 = 4

Coordenada y = (by1 + ay2) / (a + b) donde (y1, y2) = (1,9)

Conectando estos valores que tenemos; (4 (1) + 1 (9)) / (1 + 4) = (4 + 9) / 5 = 13/5

Por lo tanto, las coordenadas del punto es (4,13 / 5)

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Given:

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Solution:

In a right angle triangle,

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mojhsa [17]

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2 years ago

Read 2 more answers

Solve the system of linear equations for x and y.(cos θ)x + (sin θ)y=1(−sin θ)x + (cos θ)y = 0x=y=

lys-0071 [83]

Answer:

$\bold{x =cos\theta}\\\bold{y=sin\theta}$

Step-by-step explanation:

The given system of linear equations is:

$(cos\theta)x+(sin\theta)y=1\\(-sin\theta)x+(cos\theta)y=0$

We have to solve the equations for the values of $x, y$ .

Let us use elimination method in which we eliminate one of the variables from the two variables.

For this, let us multiply the first equation by $sin\theta$ and second equation by $cos\theta$

Now, the equations become:

$(cos\theta.sin\theta)x+(sin\theta.sin\theta)y=sin\theta\\\Rightarrow (cos\theta.sin\theta)x+(sin^2\theta)y=sin\theta ....... (1)\\\\(-sin\theta.cos\theta)x+(cos\theta.cos\theta)y=0\\\Rightarrow (-sin\theta.cos\theta)x+(cos^2\theta)y=0 ..... (2)$

Now, let us add (1) and (2):

$(sin^2\theta)y+(cos^2\theta)y=sin\theta\\\Rightarrow (sin^2\theta+cos^2\theta)y=sin\theta\\\Rightarrow (1)y=sin\theta\\\Rightarrow y = sin\theta$

Using the equation:

$(-sin\theta)x+(cos\theta)y=0$

Putting value of $y$ :

$\Rightarrow (-sin\theta)x+(cos\theta)sin\theta=0\\\Rightarrow (sin\theta)x=(cos\theta)sin\theta\\\Rightarrow x = cos\theta$

So, the answer to the system of linear equations is:

$\bold{x =cos\theta}\\\bold{y=sin\theta}$

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