**Core Concept**
Muscle weakness and difficulty in physical activities, along with specific dermatomyositis manifestations such as heliotrope rash (not mentioned here, but implied by the maculopapular rash over MCP joints), suggest an underlying inflammatory myopathy. Dermatomyositis is a type of idiopathic inflammatory myopathy characterized by muscle inflammation and skin changes.

**Why the Correct Answer is Right**
The presence of Gower sign (difficulty in getting up from the floor on all fours) and muscle weakness in a child, along with the specific skin rash, points towards dermatomyositis. The next step is to investigate the muscle involvement with a muscle biopsy to confirm the diagnosis. This is because muscle biopsy is the gold standard for diagnosing inflammatory myopathies like dermatomyositis, showing characteristic histopathological changes such as muscle fiber necrosis, inflammation, and perifascicular atrophy.

**Why Each Wrong Option is Incorrect**
**Option A:** Blood tests such as creatine kinase (CK) levels can be elevated in dermatomyositis but are not diagnostic. While CK levels can support the diagnosis, they are not the next appropriate investigation.
**Option B:** Electromyography (EMG) is a useful tool for assessing muscle function and can show changes consistent with myopathy. However, it is not the definitive investigation for diagnosing dermatomyositis.
**Option C:** Magnetic Resonance Imaging (MRI) can show muscle edema and inflammation in dermatomyositis but is not as sensitive as muscle biopsy for diagnosing this condition.
**Option D:** Routine blood tests such as complete blood count (CBC) and liver function tests (LFTs) are not specific for dermatomyositis and would not be the next appropriate investigation.

**Clinical Pearl / High-Yield Fact**
In dermatomyositis, it is essential to also investigate for underlying malignancies, as there is an increased risk of associated cancers, particularly in adults but also in children.

**Correct Answer:** C. MRI.