Answer

Verified

339.9k+ views

**Hint:**In this question, you have to find the point which is three-fourth of the way from A(3,1) to B(2,5). You need to consider a variable for the three-fourth point in the way from A(3,1) to B(2,5). You can use the section formula to solve this problem. So let us see how we can solve this problem.

**Complete Step by Step Solution:**

Given that there is a three-fourth point in between A(3,1) to B(2,5). Let S be the point which is three-fourth of the way from A(3,1) to B(2,5).

So we have, AP : AB = 3 : 4

Now, AB = AP + PB

$\therefore \dfrac{{AP}}{{AB}} = \dfrac{{AP}}{{(AP + PB)}} = \dfrac{3}{4}$

On cross multiplying we get,

$\Rightarrow 4AP = 3AP + 3BP$

Subtracting 3AP from both the sides of the above expression,

$\Rightarrow 4AP - 3AP = 3BP$

$\Rightarrow AP = 3BP$

$\Rightarrow \dfrac{{AP}}{{AB}} = \dfrac{3}{1}$

So, the ration m : n = 3 : 1

${x_1} = 3,{y_1} = 1,{x_2} = 2,{y_2} = 5$

By section formula we get: $x = \dfrac{{m{x_2} + n{x_1}}}{{m + n}}$

Putting all the values of the variable in the above expression we get,

$\Rightarrow x = \dfrac{{3 \times 2 + 1 \times 3}}{{3 + 1}}$

After addition and subtraction, we get,

$\Rightarrow x = \dfrac{9}{4}$

By section formula we get: $y = \dfrac{{m{y_2} + n{y_1}}}{{m + n}}$

$\Rightarrow y = \dfrac{{3 \times 5 + 1 \times 1}}{{3 + 1}}$

After addition and subtraction, we get,

$\Rightarrow y = \dfrac{2}{4}$

Therefore, $y = \dfrac{1}{2}$

**So the coordinate of P is $(\dfrac{9}{4},\dfrac{1}{2})$.**

**Note:**

In the above solution we have used the section formula. The sectional formula is $M(x,y) = (\dfrac{{m{x_2} + n{x_1}}}{{m + n}},\dfrac{{m{y_2} + n{y_1}}}{{m + n}})$. In the question, it is given that the point is three-fourth from A(3,1) to B(2,5). Section formula is used when we have to find the ratio in which the line segment is divided by a point externally or internally.

Recently Updated Pages

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE

What are the possible quantum number for the last outermost class 11 chemistry CBSE

Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE

What happens when entropy reaches maximum class 11 chemistry JEE_Main

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Give simple chemical tests to distinguish between the class 12 chemistry CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How will you bring about the following conversions class 12 chemistry CBSE

Consider a system of two identical particles One of class 11 physics CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

State the laws of reflection of light