3D Geometry
Reflection and Intersection of Lines
Grade 12
Question:
<p>Two lines \(\frac{x - 3}{1} = \frac{y + 1}{3} = \frac{z - 6}{-1}\) and \(\frac{x + 5}{7} = \frac{y - 2}{-6} = \frac{z - 3}{4}\) intersect at the point R. The reflection of R in the xy-plane has coordinates</p>
<p>(a) \((2, -4, -7)\)</p>
<p>(b) \((2, -4, 7)\)</p>
<p>(c) \((-2, 4, 7)\)</p>
<p>(d) \((2, 4, 7)\)</p>
Step-by-Step Solution
Key Concept: Find the intersection point R first, then reflect it in the xy-plane by changing the sign of the z-coordinate.
Find the intersection point R of the two lines. Reflection in the xy-plane changes the sign of the z-coordinate only.
Correct Answer: A