Question

find the ratio in which the straight line 3x-4y=7 divides the join of (2,-7) and (-1,3) for 2 marks.​

Answer 1

Answer:

The straight line divides the join of given points in the ratio 27:22

Step-by-step explanation:

The equation of the straight line is $3x-4y-7=0$ and the points whose join is divided by the given line are (2,-7) and (-1,3).

Let us assume that the line divides the join of given points in the ratio $\alpha:1$.

Hence by using section formula,The point of intersection the line and the join of both points is found as follows

$P(x,y)=(\frac{\alpha(-1)+1(2)}{\alpha+1} ,\frac{\alpha(3)+1(-7)}{\alpha+1} )\\=(\frac{2-\alpha}{\alpha+1}, \frac{3\alpha-7}{\alpha+1} )$

We also know that,the above point lies on the line $3x-4y-7=0$ hence substituting them we get

$3(\frac{2-\alpha}{\alpha+1})-4( \frac{3\alpha-7}{\alpha+1} )-7=0\\= > {6-3\alpha-12\alpha+28-7\alpha-7}=0\\= > \alpha=\frac{27}{22}$

Therefore,

The straight line divides the join of given points in the ratio 27:22

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