Mathematics: Point C (4, 2) divides the line segment joining points A (2, -1) and B (x, y) such that AC: CB = 3.1 what are the coordinates of point B?

Point C (4, 2) divides the line segment joining points

Ответ:

OkK1510

18.01.2022

Mathematics

The coordinates of B are $(\frac{14}{3} ,3)$ .

Solution:

Given A(2, –1), B(x, y) and C(4, 2)

AB is a line segment C is a point on AB.

AC : CB = 3 : 1

To find the coordinates of B:

Section formula:

The point P(x,y) divides the line segment A(x_1,y_1) and B(x_2,y_2) in the ratio

m : n are $\left(\frac{\mathbf{m} \mathbf{x}_{2}+\mathbf{n} \mathbf{x}_{\mathbf{1}}}{\mathbf{m}+\mathbf{n}}, \frac{\mathbf{m} \mathbf{y}_{2}+\mathbf{n} \mathbf{y}_{\mathbf{1}}}{\mathbf{m}+\mathbf{n}}\right)$

Here, $x_1=2, \ x_2=x, \ x_3=4, \ y_1=-1, \ y_2=y, \ y_3=2$ and m = 3, n = 1

Using section formula,

$$C(x_3,y_3)=\left(\frac{mx_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right)$

Substitute the given values in the section formula.

$$C(4,2)=\left(\frac{3 \times x+1 \times 2}{3+1}, \frac{3 \times y+1 \times (-1)}{3+1}\right)$

$$C(4,2)=\left(\frac{3x+2}{4}, \frac{3y-1}{4}\right)$

Equate the x-coordinates and y-coordinates.

$$\frac{3x+2}{4}=4, \ \ \ \frac{3y-1}{4}=2$

$$\ 3x+2=16, \ \ \ \ 3y-1=8$

$$ 3x=14, \ \ \ \ 3y=9$

$$ x=\frac{14}{3}, \ \ \ \ y=3$

Hence the coordinates of B are $(\frac{14}{3} ,3)$ .

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Ответ:

balancingmist1827

23.03.2022

Mathematics

x = 5

Step-by-step explanation:

Pythagorean Theorem:

a² + b² = c²

12² + b² = 13²

144 + b² = 169

b² = 25

b = 5

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-Chetan K

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Point C (4, 2) divides the line segment joining points A (2, -1) and B (x, y) such that AC: CB = 3.1 what are the coordinates of point B?

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