Chapter 4.5, Problem 74E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Distance A line with slope m passes through the point (0,-2).(a) Write the distance d between the line and the point (4, 2)as a function of m. (Hint: See Section 1.2, Exercise 77.)(b) Use a graphing utility to graph the equation in part (a).(c) Find lim m → ∞ d ( m ) and lim m → − ∞ d ( m ) . Interpret the resultsgeometrically.

(a)

To determine

To calculate: The distance between the line and the provided point (4,2).

Explanation

Given:

A line with slope m that passes through (0,âˆ’2) and the point (4,2).

Formula used:

The distance d, between a point (a,b) and a line Ax+By+C=0 is given by the formula:

d=|Aa+Bb+C|A2+B2

Calculation:

The line has a slope m and passes through the point (0,âˆ’2).

From the point-slope form of the line, its equation would be:

y+2=m(xâˆ’0)y+2=mx</

(b)

To determine

To graph: The equation obtained in part (a).

(c)

To determine

To calculate: The provided limits limmd(m),limmd(m) and their geometrical interpretation.

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