Step 1: Read the lab pattern.
The child has rickets that does not respond to plain vitamin D, so this is vitamin D refractory (resistant) rickets. The calcium is 9 mg/dl, which is normal. The phosphate is 2.4 mg/dl, which is low for a child. The alkaline phosphatase is 1040 IU, which is very high and points to active bone turnover. Parathyroid hormone and bicarbonate are both normal.
Step 2: Rule out renal tubular acidosis.
Both distal and proximal renal tubular acidosis make the kidney lose bicarbonate or fail to excrete acid, so blood bicarbonate falls and the child develops metabolic acidosis. Here bicarbonate is normal, so neither distal RTA nor proximal RTA fits. This rules out options (A) and (D).
Step 3: Rule out vitamin D dependent rickets.
Vitamin D dependent rickets (type 1 or type 2) comes from a defect in making or responding to active vitamin D. This drops the blood calcium, and low calcium then drives up parathyroid hormone as the body tries to correct it. Here calcium is normal and PTH is normal, so this pattern does not match option (C).
Step 4: Match the pattern to hypophosphatemic rickets.
Hypophosphatemic rickets (the X-linked form is the most common type) comes from excess loss of phosphate through the kidney. The classic picture is normal calcium, low phosphate, normal PTH, normal acid-base status, and a high alkaline phosphatase from ongoing rickets activity. This fits the child exactly.
Final Answer:
The labs point to a phosphate-wasting disorder with normal calcium and PTH, which is Hypophosphatemic Rickets.
\[ \boxed{\text{Hypophosphatemic Rickets}} \]