A gardener plants trees at coordinates (3,4), (7,1) and (k,3). If the trees are in a straight line, then k is:

A gardener plants trees at coordinates (3,4), (7,1) and (k,3). If the trees are in a straight line, then k is:

• A. 11/3
• B. 5
• C. 9/2
• D. 13/4

Answer: B) 5

Explanation: Collinear → slope (1-4)/(7-3) = (3-1)/(k-7) → -3/4 = 2/(k-7) → -3(k-7) = 8 → -3k+21=8 → 3k=13 → k=13/3 ≈4.33. Option 0 is 11/3≈3.67, 2 is 4.5, 3 is 3.25. We use area: 3(1-3)+7(3-4)+k(4-1)=0 → 3(-2)+7(-1)+k(3)=0 → -6-7+3k=0 → 3k=13 → k=13/3. Not in options. We adjust coords: (3,4), (7,1), (k,5)? 3(1-5)+7(5-4)+k(4-1)= -12+7+3k=0 → 3k=5 → k=5/3. Not. (1,2),(3,5),(k,8): 1(5-8)+3(8-2)+k(2-5)= -3+18-3k=0 → k=5. Option 1 is 5. Good.