Question

Line stack A B with bar on top is partitioned at point C, with ratio 3:4, and its midpoint is D.

Answer 1

Easy

ok, so the midpoint formula
the midpoint of the 2 points $(x_1,y_1)$ and $(x_2,y_2)$ is
$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
so midpoint of (6,17) and (13,3) is
$(\frac{6+13}{2},\frac{17+3}{2})$=
$(\frac{18}{2},\frac{20}{2})$=
(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

$(\frac{3(6+13)}{7},\frac{3(17+3)}{7})$
$(\frac{3(18)}{7},\frac{3(20)}{7})$
$(\frac{54}{7},\frac{60}{7}$
in decimal
(7.7142857142857142857142857142857,8.5714285714285714285714285714286)


distance between (x1,y1) and (x2,y2) is
$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$
distance between (6,17) and (13,3) is
$D=\sqrt{(6-13)^2+(17-3)^2}=$
$D=\sqrt{(-7)^2+(14)^2}=$
$D=\sqrt{49+196}=$
$D=\sqrt{245}$ = $7\sqrt{5}$





point C is $(\frac{54}{7},\frac{60}{7}$ or (7.7142857142857142857142857142857,8.5714285714285714285714285714286) in decimal
point D is (9,10)
Distance between points A and B is $\sqrt{254}$ or $7\sqrt{5}$