Straight Lines
Triangle formed by lines
Grade 11
Question:
<p>Two equal sides of an isosceles triangle are given by the equations \(7x - y + 3 = 0\) and \(x + y - 3 = 0\) and its third side passes through the point \((1, -10)\), then equations of the third side can be:</p>
<p>(a) \(x - 3y - 31 = 0\)</p>
<p>(b) \(y - 3x + 13 = 0\)</p>
<p>(c) \(3x + y + 7 = 0\)</p>
<p>(d) \(y - 2x + 12 = 0\)</p>
Step-by-Step Solution
Key Concept: In an isosceles triangle, the base angles are equal, which constrains the slope of the third side given the slopes of the two equal sides.
<p>The two equal sides of the isosceles triangle are given. The base (third side) passes through \((1, -10)\). For an isosceles triangle, the angles at the base are equal. The slopes of the two given sides are 7 and -1. Using the angle bisector property or the isosceles triangle condition, we find the equations of the possible base lines.</p>
Correct Answer: a, c