Carcass wrote:
The points A( 0, 0), B( 0, 4a – 5), and C( 2a + 1, 2a + 6) form a triangle. If ∠ ABC = 90 °, what is the area of triangle ABC?
A. 102
B. 120
C. 132
D. 144
E. 156
90° is at B so area will be (AB*BC)/2
Since coordinates of x in A and B are the same that is 0, meaning A and B lie on y-axis, and 90° is at B, the y-coordinates of B and C should be the same.
So \(4a-5=2a+6.......2a=11.....a=\frac{11}{2}\)..
Now AB is nothing but y-coordinates of B and BC is nothing but x-coordinates of C
1)So X coordinates of C are \(2a+1=2*\frac{11}{2}+1=11+1=12\)
2) y coordinates of B = \(2a+6=2*\frac{11}{2}+6=11+6=17\)
Area = \(\frac{12*17}{2}=6*17=102\)
A