easy
ok, so the midpoint formula
the midpoint of the 2 points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
so midpoint of (6,17) and (13,3) is
[tex](\frac{6+13}{2},\frac{17+3}{2})[/tex]=
[tex](\frac{18}{2},\frac{20}{2})[/tex]=
(9,10)
point D is (9,10)
ok, so the other onne
this is kind of tricky but not
we must do
3:4 right?
so 3+4=7
divide the line into 7 segments and take 3 of them
Assming AC:CB=3:4
hmm, to divide the segment into 1:1, we did 1+1=2, and multiplied each sum of points by 1/2
so multiply each by 3/7
[tex](\frac{3(6+13)}{7},\frac{3(17+3)}{7})[/tex]
[tex](\frac{3(18)}{7},\frac{3(20)}{7})[/tex]
[tex](\frac{54}{7},\frac{60}{7}[/tex]
in decimal
(7.7142857142857142857142857142857,8.5714285714285714285714285714286)
distance between (x1,y1) and (x2,y2) is
[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
distance between (6,17) and (13,3) is
[tex]D=\sqrt{(6-13)^2+(17-3)^2}=[/tex]
[tex]D=\sqrt{(-7)^2+(14)^2}=[/tex]
[tex]D=\sqrt{49+196}=[/tex]
[tex]D=\sqrt{245}[/tex] = [tex]7\sqrt{5}[/tex]
point C is [tex](\frac{54}{7},\frac{60}{7}[/tex] or (7.7142857142857142857142857142857,8.5714285714285714285714285714286) in decimal
point D is (9,10)
Distance between points A and B is [tex]\sqrt{254}[/tex] or [tex]7\sqrt{5}[/tex]
