Family of lines and concurrency
Two-dimensional geometry · Mathematics
Study notes
Q: Show x+y=3, 2x−y=0, x−2y=−3 are concurrent. Find lines through (1,2): (a) through intersection of first two (b) family form. Intersect: x+y=3, 2x−y=0 → 3x=3, x=1, y=2. Check third: 1−4 = −3 ✓. Concurrent at (1,2). Family through (1,2): (x+y−3) + k(2x−y) = 0.