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Three friends Yogesh(A), Rajan(B) and Ashwani(C) were sitting in the computer room from the bottom as follows: Yogesh: First row and First column. Ashwani: Fourth row and Fourth column. Rajan: Sixth row and Sixth column. Mr. Vikas asked Munish, "are they sitting in the same line"? Munish took a ruler and tried to see whether they are in the same line or not. He was not sure as the ruler was too short for this purpose. Neha performed certain calculations and claimed that they are sitting in the same line. Based on this statement, state how she arrived at this conclusion.

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bar method

graph method

slope method

none of the above

answer is C.

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Detailed Solution

The given information from the graph states that the vertices are:

1, 1, 4, 4, 6, 6

.
We have to use the slope method in this question.
The formula of slope method is given by

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

.
If the slope of the first and third points is the same, the points are on the same line.
The slope of the first a two points is

\frac{4 - 1}{4 - 1} = \frac{3}{3} = 1

.
Slope for the first and third point is

\frac{6 - 1}{6 - 1} = \frac{5}{5} = 1

.
Since, both slopes are same, she used slope method to understand that they were sitting in the same line.
Therefore, the slope method is used.
Hence, the correct option is 3.

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