# What is the distance of the point of intersection of x + 2y = 8 and x - y = 9 from the point (4, 2)

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Expert Answers

justaguide | Certified Educator

The x and y intercepts are the same for the lines x + 2y = 8 and x - y = 9 at their point of intersection. The system of equations representing the two lines has to be solved.

Substitute x = 8 - 2y in x - y = 9

=> 8 - 2y - y = 9

=> -3y = 1

=> y = -1/3

x = 26/3

The distance of the point `(26/3, -1/3)` from (4, 2) is:

D = `sqrt((4 - 26/3)^2 + (2 + 1/3)^2)`

=> `sqrt(196/9 + 49/9)`

=> `sqrt(245/9)`

**The distance between the point (4,2) and the point of intersection of the lines x + 2y = 8 and x - y = 9 is `sqrt 245/3` **