Find the distance from the point

Question

Find the distance from the point (9, –2) to the line y = ³∕₂x + 4.

A)	units
B)	units
C)	units
D)	units

Answer 1

Find the parallel line containing (9, -2)

-2 = 3/2(9) + b ;b = -31/2; y = 3/2x - 31/2

Then, find the distance apart for these two lines

(4 - -31/2)/sqrt(1^2 + (3/2)^2) = 39/2/sqrt(13/4) = 39/2/(sqrt(13)/2) = 3 sqrt(13) or sqrt(117)

Answer 2

First, The perpendicular line has slope -2/3

It eats (9, -2)

B = y - mx

= -2 - (-2/3)(9)

= -2 - (-6)

= -2 + 6

= 4

y = (-2/3) x + 4

next,

they intersect at:

(3/2)x +4 = (-2/3)x + 4

multiplies by 6:

9x + 24 = -4x + 24

9x = -4x

x = 0

they intersect at (0,4)

finally

distance formula (0,4) vs (9,-2)

sqrt ( 9^2 + 6^2) = sqrt( 81 + 36)

= sqrt(117)