Question

Point A (1, 2) and B (3, 4) are two ends of a line segment. Find the point which divides AB in the ratio 3:4.​

Answer 1

Answer:

see the attachment for answer

Step-by-step explanation:

Your point is (x,y)=(13/7,20/7)

I hope u get your answer

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Answer 2

The point which divides the line segment AB in the ratio is O (13/7, 20/7).

Given,

two points, A(1,2) and B(3,4)

To Find,

The point which divides AB in the ratio 3:4

Solution,

This problem can be solved using the section formula in coordinate geometry.

Let the point which divides the line AB in the ratio 3:4 be O(x,y)

The section formula to find the coordinates of O(x,y) is given by the following formula:

$\implies O(x,y) = (\frac{m_1x_2 + m_2x_1}{m_1+m_2} + \frac{m_1y_2 + m_2y_1}{m_1+m_2})$

Here, The ratio m1:m2 is given to be 3:4

⇒ m1 = 3 and m2 = 4

Also, A(x1,y1) = A(1, 2) and B(x2,y2) = B(3, 4)

⇒ x1 = 1, x2 = 3, y1 = 2, and y2 = 4

Substitute these values in the section formula to get the coordinates of the required point O(x,y)

$\implies O(x,y) = (\frac{3\times3 + 4\times1}{3+4} , \frac{3\times4 + 4\times2}{3+4})\\\\\implies O(x,y) = (\frac{9 + 4}{7} , \frac{12 + 8}{7})\\\\\implies O(x,y) = (\frac{13}{7} , \frac{20}{7})$

Therefore, the required coordinates are O(13/7, 20/7)

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