The point (-1,5) is half-way between (a,-9a) and (a+3,4a). What is the value of "a"?

Question

The point (-1,5) is half-way between (a,-9a) and (a+3,4a). What is the value of  "a"?

lgbasallote · Answer

hint:
$$\huge \frac{a + (a+3)}{2} = 1$$
$$\huge \frac{-9a + 4a}2 = 5$$
does that help?

lgbasallote · Answer

solve for a

anonymous · Answer

for both?

lgbasallote · Answer

wait first one should be -1 not 1

lgbasallote · Answer

you can do both...but they'll just give you the same values for a

lgbasallote · Answer

pick whichever equation is easier for you then solve for a

anonymous · Answer

for the 1st i got a=-1/2
and the 2nd i got -2/3

lgbasallote · Answer

redo your solution...i think you did something wrong

lgbasallote · Answer

remember...first equation is = -1 not =1

anonymous · Answer

-5/2

lgbasallote · Answer

$$\huge \frac{a + (a+3)}{2} = -1$$
cross multiply
$$\huge a + a + 3 = -2$$
is this what you did?

lgbasallote · Answer

something smells fishy here

amistre64 · Answer

(a,-9a)   ( -1   ,  5  )    (a+3,4a)
-a +9a      -a   +9a       -a  +9a
------------------------
  (0,0)     (-1-a,5+9a)   (3,13a)$$-1-a=\frac{3}{2}$$

anonymous · Answer

i'm still confused

amistre64 · Answer

if I lay a pencil on the desk in front of me, it has a middle point;  if i pick up the pencil and move it to the table in the kitchen, its middle point is still the same relative to the pencil

amistre64 · Answer

my method, i moved the pencil to see it better

amistre64 · Answer

-1-a   is still half way between 0 and 3

anonymous · Answer

ok