Thursday

April 2, 2015

April 2, 2015

Posted by **Jack** on Friday, May 11, 2007 at 9:04am.

Finding the shortest distance, to two decimal places, from the point P ( 7,5) to the line 2x+3y = 18?

Thanks

The square of the distance from a point on that line, at location x, is

D^2 = (7-x)^2 + (5-y)^2

= (7-x)^2 + [-1 + (2x/3)]^2

Set the derivative dD^2/dx = 0

Solve for x and then use the equation 2x+3y = 18 to get y. Then compute D

Another way to do this is to find the equation for the line through the point P that is perpendicular to the line. Since the slope of 2x+3y = 18 is -2/3, the slope of the perpendicular is 3/2.

another way would be to use vectors.

Have you studied vectors?

There is no point to show you the method unless you know the topic.

**Answer this Question**

**Related Questions**

math - A straight line is the shortest distance between two points. In a ...

math - round result to two decimal places...the answer i have is: 7.023 so two ...

math - Consider the following bivariate data. Point A B C D E F G H I J x 3 4 2 ...

math help - Can some one help me with this one??? Consider the following ...

Urgent! MATH - Can some one please explain to me how to do this??? You are ...

statistics - Consider the following bivariate data. Point A B C D E F G H I J x ...

maths - A ship travels at a constant speed of 25 kilometers per hour (kph) in a ...

math - A map has a scale of 1/2 inch to 4 miles. The shortest distance between ...

statistics check - Consider the following bivariate data. Point A B C D E F G H ...

math - Find the exact value of the shortest distance from the origin to each ...