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

How do you: Find the shortest distance, to two decimal places from the origin to the line x - 2y = - 8 without using the formula.

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 - 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 ...
- math - A straight line is the shortest distance between two points. In a ...
- statistics - Consider the following bivariate data. Point A B C D E F G H I J x ...
- statistics check - Consider the following bivariate data. Point A B C D E F G H ...
- 12th grade math - What is the distance between the origin and the point (5, 12...
- math - Consider the following bivariate data. Point A B C D E F G H I J x 3 4 2 ...
- geometry - What is the distance between the origin and the point (5, -19)? If ...
- geometry - What is the distance between the origin and the point (5, -19)? If ...

More Related Questions