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Chapter 3: Q. 86 (page 157)

Find the point on the line y=x+1that is closest to the point 4,1.

Short Answer

Expert verified

The point on the line y=x+1closest to 1,4is2,3.

Step by step solution

01

Step 1. Given information

We need to determine the point on the line y=x+1that is closest to the point 4,1.We need to express the distance dfrom the point to the line as a function of xand then find the minimum value of dx2.

02

Step 2. Simplify

Let the line be perpendicular to the line y=x+1and y=mx+c.

Since the perpendicular lines have an inversely proportional slope.

So, m=-11.

m=-1.

The line passing through the point 4,1and having the slope -1is,

y-1=-1x-4.

y=-x+5.

Now put the point x,ythat is x,x+1in y=-x+5.

-x+1=-x+5.

2x=4.

x=2.

The point on the liney=x+1is closest to1,4is2,3.

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