Find the distance from the point $(15,-21)$(15,−21) to the line for which $f(4)=-8$f(4)=−8 and $f(8)=-18$f(8)=−18 . Round your answer to the nearest tenth.
+128460 The line contains the points ( 4, -8) and (8, -18)
The slope of this line = [ -18 - -8 ] / [ 8 - 4 ] = -10 / 4 = - 5/2
The equation of this line is
y = (-5/2) ( x - 4) - 8 multiply throrgh by 2
2y = -5 ( x - 4) - 16
2y = -5x + 20 - 16
2y = -5x + 4
Put into standard form Ax + By + C = 0
5x + 2y - 4 = 0
The distance from a point (x, y) = (15,-21) to the line is given by
l Ax + By + C l l 5 (15) + 2 (-21) -4 l l 75 - 42 - 4 l 29
______________ = ____________________ = ______________ = _____ =
√ [ A^2 + B^2 ] √ [ 5^2 + 2^2] √29 √29
√29 ≈ 5.4
