Straight Lines
Triangles and Special Points
Grade 11
Question:
<p>Let <em>A</em> ≡ (3, 2) and <em>B</em> ≡ (5, 1). ABP is an equilateral triangle constructed on the side of AB remote from the origin then the orthocentre of triangle ABP is:</p>
<p>(a) \(4 - \frac{1}{2}\sqrt{3}, -\frac{3}{2}\sqrt{3}\)</p>
<p>(b) \(4 + \frac{1}{2}\sqrt{3}, +\frac{3}{2}\sqrt{3}\)</p>
<p>(c) \(4 - \frac{1}{6}\sqrt{3}, -\frac{1}{2}\sqrt{3}\)</p>
<p>(d) \(4 + \frac{1}{6}\sqrt{3}, +\frac{1}{2}\sqrt{3}\)</p>
Step-by-Step Solution
Key Concept: Find the third vertex P of an equilateral triangle, then calculate the orthocentre which coincides with the centroid for equilateral triangles.
<p>Not provided in source text</p>
Correct Answer: a