Determine the distance between the point P(3,7) and the line 2x-5y+8=0

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We know that if P(m, n) and the line ax+by + C = 0, Then the distance is given by :

D = l ma + bn + Cl / sqrt(a^2+b^2)

Let us substitue with given info.

==> P (3, 7) and the line 2x-5y + 8 = 0

==>...

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We know that if P(m, n) and the line ax+by + C = 0, Then the distance is given by :

D = l ma + bn + Cl / sqrt(a^2+b^2)

Let us substitue with given info.

==> P (3, 7) and the line 2x-5y + 8 = 0

==> D = l 3*2 + 7*-5 + 8 l / sqrt(2^2+-5^2)

           = l 6 - 35 + 8 l / sqrt(4+25)

           = l-21l / sqrt(29) = 21/sqrt29

Then the distance between the point P and the line is 21/sqrt29 units.

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