# What is the equation of the line that consists of points equidistant from (4, 7) and (5, 9)?

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justaguide | Certified Educator

The slope of the line joining (4, 7) and (5, 9) is

m = (9 – 7)/ (5 – 4)

=> m = 2/1

=> m = 2

Therefore the slope of the line perpendicular to this is -1/2. This follows from the fact that the product of the slope of two perpendicular lines is -1.

Now the midpoint between (4, 7) and (5, 9) is [(4 + 5)/2, (9 + 7)/2] or (9/2, 8)

The line with slope -1/2 passing through (9/2, 8) is y – 8 = (-1/2)*(x – 9/2)

=> y -8 = (-1/4)*(2x – 9)

=> 4*(y – 8) = (-1)* (2x – 9)

=> 4y – 32 = 9 – 2x

=> 2x + 4y – 41 = 0

**Therefore the equation of the line that consists of points equidistant from (4, 7) and (5, 9) is 2x + 4y – 41 = 0**