Please Help How do I

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

The answer is A. We can use the points (9,0) and for the equation substitute 0 for x and y=4.

then substituting into the distance formula we get answer A.

Answer 2

The shortest distance is along the normal (perpendicular)

y = -2x/3 + b

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

-2 = -6 + b

4 = b

y = -2x/3 + 4

-2x/3 + 4 = 3x/2 + 44

x = 0

y = 4

d² = (0 - 9)² + (4 + 2)²

d² = 81 + 36

d² = 117