ICSE Board Question Based on Equation of a Straight Line Chapter of M.L Aggarwal for class10

In this question a line given that is parallel and passes through the mid-point of the line segment joining the points given as per the question.

This is the Question Number 19, Exercise 12.2 of M.L Aggarwal.

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# Find the equation of the line that is parallel to 2x + 5y – 7 = 0 and passes through the mid-point of the line segment joining the points (2, 7) and (– 4, 1).

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Given line: 2x + 5y – 7 = 0

5y = -2x + 7

y = (-2/5) x + 7/5

So, the slope is -2/5

Hence, the slope of the line that is parallel to the given line will be the same, m = -2/5

Now, the mid-point of the line segment joining points (2, 7) and (– 4, 1) is

((2 – 4)/2, (7 + 1)/2) = (-1, 4)

Thus, the equation of the line will be

y – y

_{1}= m (x – x_{1})y – 4 = (-2/5) (x + 1)

5y – 20 = -2x -2

2x + 5y = 18