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Point A is located at (2,14) and Point B is located at (17,4). what point partitions the directed line segment AB into a 4:1 ratio. Write your coordinates with no spaces EX. (1,5)​

Respuesta :

Answer:

To find the point that partitions the directed line segment AB into a 4:1 ratio, we use the section formula.

Let the point dividing the line segment AB be (x, y). According to the section formula, the coordinates of this point can be calculated using the following equations:

\[ x = \frac{{x_1 \cdot m_2 + x_2 \cdot m_1}}{{m_1 + m_2}} \]

\[ y = \frac{{y_1 \cdot m_2 + y_2 \cdot m_1}}{{m_1 + m_2}} \]

Where:

- \( (x_1, y_1) \) = coordinates of point A = (2, 14)

- \( (x_2, y_2) \) = coordinates of point B = (17, 4)

- \( m_1 = 4 \) (ratio of the segment A to the partition point)

- \( m_2 = 1 \) (ratio of the segment B to the partition point)

Substituting the given values:

\[ x = \frac{{2 \cdot 1 + 17 \cdot 4}}{{4 + 1}} \]

\[ x = \frac{{2 + 68}}{{5}} = \frac{{70}}{{5}} = 14 \]

\[ y = \frac{{14 \cdot 1 + 4 \cdot 4}}{{4 + 1}} \]

\[ y = \frac{{14 + 16}}{{5}} = \frac{{30}}{{5}} = 6 \]

So, the point that partitions the directed line segment AB into a 4:1 ratio is (14,6).

shaelovesyouu

✰Answer:

(3x-2) and (x-1)

✰Step-by-step explanation:

To factorize the trinomial 3x^2 - 5x + 2, we need to find two binomial factors that, when multiplied together, result in the given trinomial.

We can find these factors by looking for two numbers that multiply to give 2 (the constant term) and add up to give -5 (the coefficient of the linear term).

The numbers that satisfy this condition are -2 and -1.

Therefore, the factorization of 3x^2 - 5x + 2 is:

(3x - 2)(x - 1)

In this factorization, (3x - 2) and (x - 1) are the two binomial factors that can be multiplied together to obtain the original trinomial.

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