# Find the distance between the points on the line 2x-3y-17=0 where x=-3 and where y=10

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Expert Answers

samhouston | Certified Educator

First, we need to establish the coordinates of the two points.

2x - 3y = 17 where x = -3

2(-3) - 3y = 17

-6 - 3y = 17

-3y = 23

y = -23/3

first point: (-3, -23/3)

2x - 3y = 17 where y = 10

2x - 3(10) = 17

2x - 30 = 17

2x = 47

x = 47/2

second point: (47/2, 10)

The distance between two points can be found using the formula:

sqrt[(x1 - x2)^2 + (y1 - y2)^2]

sqrt[(-3 - 47/2)^2 + (-23/3 - 10)^2]

sqrt(-53/2^2 + -53/3^2)

sqrt(702.25 + 312.111)

sqrt(1014.36111)

`~~`** 31.85**