Geometry please help with solution

Question

Right triangle ABC is on a plane. Segment AB is on the line y=2 and is 3 units long. Point C is on the line x=-1. If the area of ABC is 6 square units, then find possible y coordinate C.

Answer 1

two possible points for C: (-1,-2) and (-1,6)

Since AB = 3, and ABC is a right triangle, A is (-1,2) and B is (2,2) AB=3

(alternatively you could switch A and B, but it doesn't make any difference,

or you could make the 3 units of AB go to the left rather than the right, but

it makes no difference. You'll get the same points for C either way)

Area = 1/2 AB x AC = 1/2x3xAC =3/2 AC = 6

AC = 2/3 x 6 = 4

Add or subtract 4 from 2, the y coordinate of A (-1,2)

that gives C as (-1,6) or (-1, -2)

The vertical side of the right triangle is 4

The horizontal side is 3

one half of 3 x 4 is the area = 1/2 of 12 = 6

Answer 2

Let's say that AB is one leg of the right triangle( Base) and AC is the other leg.(Height)

AB = 3 units Area = 1/2 BH = 6 So BxH = 12

We said that the base, AB is 3 (3) H = 12 H= 4

Pt A is at (-1,2) so Pt C = (-1, [2-4]) = (-1,-2) or (-1, [2+4]) , (-1,6)