we have the points
A (1,-2) and B(5,3)
Find out the point (x,y) that divide the segment AB in a ratio 2:3
that means
AX/XB=2/3
step 1
Find out the horizontal distance AB
ABx=5-1=4 units
Find out the vertical distance AB
ABy=3-(-2)=5 units
step 2
we have that
the horizontal distance between A and x is
AX/XB=2/3
AX=(2/3)XB -----> equation 1
AX+XB=4 -----> equation 2
substitute equation 1 in equation 2
(2/3)XB+XB=4
(5/3)XB=4
XB=12/5
XB=2.4
the x-coordinate of X is
x=5-2.4=2.6
Find out the y-cpoordinate
AX=(2/3)XB -----> equation 1
AX+XB=5 ------> equation 2
substitute equation 1 in equation 2
(2/3)XB+XB=5
5/3(XB)=5
XB=3
the y-coordinate of X is
y=3-3=0
answer is
the coordinate of the point is (2.6,0)
answer is option A