If the points (-1, 1), (3,-2), and (q,4) are collinear, the value of q is

  q = -5

Step-by-step explanation:

For A the midpoint between B and C, we have ...

  A = (B+C)/2

  C = 2A -B

Point A(-1, 1) is the midpoint* between C(q, 4) and B(3, -2), so the point (q, 4) will be ...

  (q, 4) = 2A -B

  (q, 4) = 2(-1, 1) -(3, -2) = (2(-1)-3), 1(1)+2)

  (q, 4) = (-5, 4)

  q = -5

_____

* We know A is the midpoint because we observe the differences in y-values for C-A and A-B are ... 4 -1 = 3, and 1 -(-2) = 3. That is, points C and B are the same distance from A.

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.