(a) Let (x, yo) be a point of the plane, and let L be the graph of the function f(x) = mx + 6. Find the point i such that the distance from (x, Ja) to (, f(7)) is smallest. [Notice that minimizing this distance is the same as minimizing its square. This may simplify the computations somewhat.] (b) Also find 7 by noting that the line from (x, ya) to (F, f(x)) is perpen- dicular to L. (c) Find the distance from (x» yo) to L, i.e., the distance from (xe, ya) to (x, f(x)). [It will make the computations easier if you first assume that 6 = 0; then apply the result to the graph of f(x) – mx and the point (xa, ya - 6).] Compare with Problem 4-22. (d) Consider a straight line described by the equation Ax+ By +C = 0 (Problem 4-7). Show that the distance from (x, yo) to this line is (Ax, + By. + C)/V4² + B³. %3!
(a) Let (x, yo) be a point of the plane, and let L be the graph of the function f(x) = mx + 6. Find the point i such that the distance from (x, Ja) to (, f(7)) is smallest. [Notice that minimizing this distance is the same as minimizing its square. This may simplify the computations somewhat.] (b) Also find 7 by noting that the line from (x, ya) to (F, f(x)) is perpen- dicular to L. (c) Find the distance from (x» yo) to L, i.e., the distance from (xe, ya) to (x, f(x)). [It will make the computations easier if you first assume that 6 = 0; then apply the result to the graph of f(x) – mx and the point (xa, ya - 6).] Compare with Problem 4-22. (d) Consider a straight line described by the equation Ax+ By +C = 0 (Problem 4-7). Show that the distance from (x, yo) to this line is (Ax, + By. + C)/V4² + B³. %3!
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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