Answer:
q = -5
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
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* 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.