SOLUTION: Analytic Geometry 10. Determine the shortest distance from the point (5, 2) to the line represented by y=2x+1. Use a diagram to check your answer. Can u please help me with this

Question 200404: Analytic Geometry
10. Determine the shortest distance from the point (5, 2) to the line represented by y=2x+1. Use a diagram to check your answer.
Can u please help me with this question?
thanksss
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The distance from a point to a line is the length of the line segment between the given point and the point of intersection of a line perpendicular to the given line that contains the given point with the given line.

Step 1: Solve the given equation for

to put the equation into slope intercept form (this is already done for you), then determine the slope of the given line by inspection of the coefficient on

.

Step 2: Use

to calculate the slope of a line perpendicular to the given line.

Step 3: Write an equation of the line perpendicular to the given line that passes through the given point using the point-slope form of the equation of a line:

Step 4: Using the equation of the given line and the equation of the line just derived in step 3, solve the system of equations for the point of intersection.

Step 5: Use the distance formula to calculate the distance between the point of intersection derived in Step 4 and the given point.

John

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