Straight Lines
Orthocentre
Grade 11
Question:
<p>If a triangle ABC has vertices <span>A(-1, 7)</span>, <span>B(-7, 1)</span> and <span>C(5, -5)</span>, then its orthocentre has coordinates</p>
<p>(a) <span>(3, -3)</span></p>
<p>(b) <span>(-3, 3)</span></p>
<p>(c) <span>\left(-\frac{3}{5}, \frac{3}{5}\right)</span></p>
<p>(d) <span>\left(\frac{3}{5}, -\frac{3}{5}\right)</span></p>
Step-by-Step Solution
Key Concept: The orthocentre is found by finding the intersection of two altitudes. An altitude is perpendicular to a side and passes through the opposite vertex.
<p><strong>Solution approach:</strong> The orthocentre is the intersection point of altitudes. Find the slopes of two sides, then find equations of altitudes perpendicular to these sides passing through opposite vertices, and solve simultaneously.</p>
Correct Answer: A