analytic geometry. pls help?

Draw the line on axes system.

The segment's length is given by the distance formula:

√((-1-2)^2 + (4-(-2))^2) = √45

That means the line will be in total 4√45 long once you have extended it three times its own length. Since it says "FROM (-1,4) to (2,-2)" you know the terminal point (endpoint) will (like (2,-2)) also be in the 4th quadrant.

The easiest way to determine the terminal point is to go to the right 3 times 3 = 9 units from 2 to get 11 for your x value and to go down 3 times 6 = 18 units from -2 to get -20 for your y value.

I repeat, draw the diagram, it will increase your understanding.

Answer: Terminal point (11,-20)

Test: Length = √(-1-11)^2 + (4-(-20))^2) = √720

= √(16)(45) = 4√45

All the best and keep telling yourself: "Math is much easier than the words describing it."

First I'll assume that P1 is the point (-1,4) and P2 is the point (2,-2). The slope of the line from P1 to P2 is given by the change in the x values over the change in the y values.

m = [2 - (-1)] / (-2 - 4) = 3/-6

The slope is important because using it is the easiest way to solve the problem.

Try these steps:

1. Get a blank piece of paper and pencil. Any paper works, but graph paper is better.

2. Plot points 1 and 2 using the xy-coordinate system, and then draw a line from P1 to P2. The result will be a line that slopes downward; that is, if you dropped an object on to it, it would slide down and to the right.

Notice that you have moved to the right 3 places in the x direction and down 6 places in the y direction. This means you have used the slope to complete a line segment that ends at the point (2,-2).

4. From the point (2, -2), move to the right 3 places and down 6 places to end at the point (5,-8). You now have a line that is twice as long as the one you started with.

5. From the point (5, -8), again move to the right 3 and down 6 to end at the point (8,-14). You now have a line that is 3 times as long as the one you started with whose terminal point is the point (8,-14).

You needed 2 strategies. the only already published makes use of the line of centres and measures the radius out alongside it. the 2nd answer is the extra direct way, i think of. It starts off with the final equation of a circle with centre at (p, q) (x - p)² + (y - q)² = 2 ..... ...... (improve the brackets) x² - 2px + p² + y² - 2qy + q² = 2 ...... ...... ...... equation (A) because of the fact the Circle is going in the process the factor (a million, 3), exchange for x and y : a million - 2p + p² + 9 - 6q + q² = 2 p² + q² - 2p - 6q + 8 = 0 ..... ..... ..... ..... equation (B) ..... ..... ..... ..... ..... ..... ..... ..... ..... If we differentiate eqn. (A) : ..... ..... ..... ..... ..... ..... ..... ..... ..... 2x - 2p + 2y(dy/dx) - 2q(dy/dx) = 0 ..... ..... ..... ..... ..... ..... ..... ..... ..... The slope of the tangent (x + y = 4) is -a million, ..... ..... ..... ..... ..... ..... ..... ..... ..... and it is going by way of (a million, 3), so substituting ..... ..... ..... ..... ..... ..... ..... ..... ..... those values we get : ..... ..... ..... ..... ..... ..... ..... ..... ..... 2 - 2p + 6(-a million) + 2q = 0 ..... ..... ..... ..... ..... ..... ..... ..... ..... - 2p + 2q = 4 ..... ..... ..... ..... ..... ..... ..... ..... ..... - p + q = 2 ..... ..... ..... ..... ..... ..... ..... ..... ..... So q = p + 2 Substituting for q in equation (B) : p² + (p + 2)² - 2p - 6(p + 2) + 8 = 0 p² + p² + 4p + 4 - 2p - 6p - 12 + 8 = 0 2p² - 4p = 0 p (p - 2) = 0 consequently p = 0 or p = 2 while p = 2, q = 0, and while p = 2, q = 4. the two circles are ..... x² + (y - 2)² = 2 ..... ..... ..... ..... ..... ... ..... (x - 2)² + (y - 4)² = 2