The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC=90`, what is the area of triangle ABC?
A. 102
B. 120
C. 132
D. 144
E. 156
[spoiler]this was extracted from the BTG problem set; the official explanation suggests drawing an arbitrary line AB which is horizontal and setting y coordinates for the points B and C as equal. Instead, I look into the slop relationship of lines B and C since the two must form an angle and their line directions must be opposite which means crossing of lines B and C at some point to form the vertice => now we may set y-coordinates as equal for B and C!
p.s. this problem could be complicated by drawing multiple lines in the xy-rectangular coordinate system and having all lines be related with themselves - the approach of arbitrary line(s) would not fit then[/spoiler]
A. 102
B. 120
C. 132
D. 144
E. 156
[spoiler]this was extracted from the BTG problem set; the official explanation suggests drawing an arbitrary line AB which is horizontal and setting y coordinates for the points B and C as equal. Instead, I look into the slop relationship of lines B and C since the two must form an angle and their line directions must be opposite which means crossing of lines B and C at some point to form the vertice => now we may set y-coordinates as equal for B and C!
p.s. this problem could be complicated by drawing multiple lines in the xy-rectangular coordinate system and having all lines be related with themselves - the approach of arbitrary line(s) would not fit then[/spoiler]
