Question

Find the distance from the given point to the given line. Estimate your answer to the nearest 2 decimal places.

Answer 1

There are many points to create a line. Which point on the line do you want to find the distance to?

Answer 2

The distance formula:
\[
d = \sqrt{(x_1-x_2)^2+(y_2-y_1)^2}
\]
Let \((x_1, y_1) = (x, -2x+7)\) and \((x_2, y_3) = (-6, 4)\)
\[
d(x) = \sqrt{[(x)-(-6)]^2+[(-2x+7)-(4)]^2}
\]
This is the distance with respect to \(x\).
Use calculus to minimize this equation.
The distance would be the minimum value.

Answer 3

distance formula is just pythogeoren theriom

Answer 4

Another way you could do this is to create a line which is perpendicular to \(y=-2x+7\) and goes through the point \((-6, 4)\). Then find the intersection between this perpendicular line and \((-6, 4)\).

This intersecting point is going to be the closes point on \(y=-2x+7\) to \((-6, 4)\).
So just plug those two points into the distance formula.

Answer 5

Yet another way to do this is to rotate the line and the point to be parallel to the x axis. Then the line would be a constant \(y=c\) and the point would be relocated to \((x_0, y_0)\). The distance would just be \(|c-y_0|\) in this case.

Answer 6

plug what?

Answer 7

Which method are you using?

Answer 8

idk .. I'm confused here

Answer 9

could someone please break it down?

Answer 10

Usually your class should prescribe a method to use... what are you learning in class right now?