Question

in what ratio does the point ( -3,7) divide the line joining of (-5,11) and (4,-7) internally.

Answer 1

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Answer 2

Concept

A straight line is an endless length line that doesn't have any curve on it. A straight line can be formed using two points also. In geometry section formula is used to determine the ratio in which the line is divided by a point externally or internally.

Given

Point (-3,7) divides the line joining (-5,11) and (4,-7) internally

Find

Ratio of the point dividing internally

Solution

Consider a Line AB having A (-5,11) and B(4,-7) and point M(-3,7) divides the line internally in the ratio k : 1

Using Section Formula

M(-3,7) = (4k-5 / k+1 , 11-7k / k+1)

Comparing x

-3= 4k-5 / k+1

-3k-3 = 4k -5

-3+5 = 7k

2 = 7k

k=2/7

Comparing y

7 = 11 - 7k / k+1

7k+7 = 11-7k

14k = 4

k = 2/7

k : 1 = 2 : 7

Hence M(-3,7) divides the line AB in the ratio 2 : 7

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