Analytic Geometry, For my Exams:(

[simpleguy123]

I have been trying to answer this for days I still dont understand how to solve it.1. The segment for (-1,4) to (2,-2) is extended three times its own length. Find the terminal point. Thank you for your help in advance

 

[simpleguy123]

Yes I calculated the Distance

I calculated the distance with distance formula, and the result was 3squareroot5... what should i do next should i multiply it with 3? How can i get a coordinate by just knowing the distance??

 

[HallsofIvy]

You don't need to calculate its length- in fact that doesn't help. Use "similar triangles". If you were to draw a horizontal line through (-1, 4) and a vertical line through (2, 2), you get a right triangle. Assuming that you are extending this line to the right, if you draw a vertical line through the new end point you will have a larger right triangle having the same angle so "similar triangles". Since the hypotenuse of one triangle is 3 times the length of the hypotenuse of the other, the two horizontal and vertical sides are also.

 

[Steven G]

Are you able to calculate distance from (-1,4) to (2,-2) ?

What is the change in x between the two given points? What is the change in y using the two given point. If you extend it by 3 times then what should the change in x and the change in y now be? Use this info to find the terminal point. If you and your friend do this problem correctly, do you have to get the same results??

 

[simpleguy123]

Thank you guys

3SQRT(5) is correct: wanted to see if you knew how!
Can you "see" than the procedure really uses the Pythagorean Theorem?
Like, with given points A(-1,4) and B(2,-2), you can add point C(-1,-2)
thus creating a right triangle with legs AC = 6 and BC =3,
so hypotenuse AB = SQRT(6^2 + 3^2) = 3SQRT(5).

Keep that in mind and follow HallsofIvy's advice and you should be ok.

I found out that when you extend that line, you can simply make a triangle by forming the slope which is equal to rise and run. Therefore making it three times.

 

[Steven G]

You are given (-1,4) and (2,-2). Since x goes from -1 to 2 then the change in x is 3. Since you want to extend 3 times you multiply the 3 by 3 and get +9.
Since y goes from 2 to -2 then the change in y is -4. Multiply this -4 by 3 and get -12.

Now take (-1,4) and compute (-1+9, 4 -12)= (8,-8) = answer