Question

Good morning. I have another math problem I just need checked a bit please until I learn how to check and get proficient at checking with the distance formula.
#9
Given segment XZ with X(-4, 3) and Z(6, -2), find the coordinates of Y if Y divides XZ one-fifth of the way from X to Z.
-4 + 1/5 (6 - -4)
-4 + 1/5 (10)
-4 + 10/5
-4 + 2= -2
X=-2

3 + 1/5 (-2 -3)
3 + 1/5 (-5)
3 + -5/5
3 + -1 = 2
Y=2

Are my answers correct?

Answer 1

change in x = 10/5 =2 so x = -2
change in y = -5/5 = -1 so y = 2
So I agree

Answer 2

Hello Damon is this the easiest way to double check the answers by doing change in x and change in y or do you have to use the distance formula to check your answers?

Answer 3

You do not need the distance formula.

Answer 4

in general
1/5 of distance from (x1,y1) to (x2,y2)
D = sqrt [(x2-x1)^2 + (y2-y1)^2 ]
we want d = D/5
if xf = (x2-x1)/5 and yf = (y2-y1)/5
d = sqrt [ (x2-x1)^2/ 25 + (y2-y1)^2 / 25 ]
d = 1/5 sqrt [(x2-x1)^2 + (y2-y1)^2 ] sure enough