Find the point, m, that is five-sixths of the distance from a(-7, 2) to b(-1, -4). a) (-1, -3) b) (-2, -3) c) (-1, -4) d) (-2, -4)

Firstly, how many units apart is -7 from -1 (the x-coordinates)? That would be 6 units away. Multiply 5/6 by 6:

Next, how many units apart is 2 from -4? That would be, again, 6 units. Multiply 5/6 by 6.

Now, since from -7 to -1 it's increasing, add 5 to -7:

-2 is the x-coordinate of M.

Next, since from 2 to -4 it's decreasing, subtract 5 from 2:

-3 is the y-coordinate of M.

Putting it together, M is at (-2,-3), or B.

the probability is 0

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1