Please see the attached file for the full problem.How can I use a scalar projection to show that the distance from a point?P[1](x[1], y[1]) to the line 3*x-4*y+5 = 0 is > abs(a*x[1]+b*y[1]+c)/sqrt(a^2+b^2);The trick is to draw a vector B along the line between two points. One is completely arbitrary (x0,y0) and the other is the point on the line (x2,y2) which is closest to the point (x1,y1)Then, the vector between (x1,y1) and (x2,y2) must be perpendicular to the vector between (x0,y0) and (x2,y2)

This means that their dot product must be zero.

This gives you one condition.

The other conditions come from the fact that (x0,y0) and (x2,y2) must satisfy the lines equation as well.So once you set all the conditions you will be able to express x2-x1 in terms of (x1,x2) , and (y1-y2) in terms of (x1,x2) and things are pretty straight forward from there.The files attached have the full derivations and explanations.Cheers

Yinon

#### Why Choose Us

- 100% non-plagiarized Papers
- 24/7 /365 Service Available
- Affordable Prices
- Any Paper, Urgency, and Subject
- Will complete your papers in 6 hours
- On-time Delivery
- Money-back and Privacy guarantees
- Unlimited Amendments upon request
- Satisfaction guarantee

#### How it Works

- Click on the “Place Order” tab at the top menu or “Order Now” icon at the bottom and a new page will appear with an order form to be filled.
- Fill in your paper’s requirements in the "
**PAPER DETAILS**" section. - Fill in your paper’s academic level, deadline, and the required number of pages from the drop-down menus.
- Click “
**CREATE ACCOUNT & SIGN IN**” to enter your registration details and get an account with us for record-keeping and then, click on “PROCEED TO CHECKOUT” at the bottom of the page. - From there, the payment sections will show, follow the guided payment process and your order will be available for our writing team to work on it.