Question

The end points of AB are A(-2,-3) , B(3,2) point C lies on AB and is 2/5 of the way from A to . What is the coordinates of point C? Explain how you find your answer

Answer 1

x = x1+rx2/1+r ; y = y1+ry2/1+r   donde r es la razón 
aplicando la formula anterior las coordenadas serian x= -4/7 ; y=-11/7
donde x1 es la primera componente de punto A x2 la segunda componente del punto A y así mismo con Y

Answer 2

check the picture below.

$\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ A(-2,-3)\qquad B(3,2)\qquad \qquad 2:5 \\\\\\ \cfrac{AC}{CB} = \cfrac{2}{5}\implies \cfrac{A}{B} = \cfrac{2}{5}\implies 5A=2B \\\\\\ 5(-2,-3)=2(3,2)\\\\ -------------------------------$

$\bf { C=\left(\cfrac{\textit{sum of "x" values}}{r1+r2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{r1+r2}\right)}\\\\ -------------------------------\\\\ C=\left(\cfrac{(5\cdot -2)+(2\cdot 3)}{2+5}\quad ,\quad \cfrac{(5\cdot -3)+(2\cdot 2)}{2+5}\right)$