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Sveta_85 [38]
3 years ago
6

What is the ratio in which the point P(3/4,5/12) decides the line segment joining points A(1/2,3/2) and B(2,-5)

Mathematics
1 answer:
timama [110]3 years ago
6 0

Given:

The point P\left(\dfrac{3}{4},\dfrac{5}{12}\right) divides the line segment joining points A\left(\dfrac{1}{2},\dfrac{3}{2}\right) and B(2,-5).

To find:

The ratio in which he point P divides the segment AB.

Solution:

Section formula: If a point divides a segment in m:n, then the coordinates of that point are,

Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)

Let point P divides the segment AB in m:n. Then by using the section formula, we get

\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{m(2)+n(\dfrac{1}{2})}{m+n},\dfrac{m(-5)+n(\dfrac{3}{2})}{m+n}\right)

\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{2m+\dfrac{n}{2}}{m+n},\dfrac{-5m+\dfrac{3n}{2}}{m+n}\right)

On comparing both sides, we get

\dfrac{3}{4}=\dfrac{2m+\dfrac{n}{2}}{m+n}

\dfrac{3}{4}(m+n)=\dfrac{4m+n}{2}

Multiply both sides by 4.

3(m+n)=2(4m+n)

3m+3n=8m+2n

3n-2n=8m-3m

n=5m

It can be written as

\dfrac{1}{5}=\dfrac{m}{n}

1:5=m:n

Therefore, the point P divides the line segment AB in 1:5.

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