Answer:
(b) 4
Step-by-step explanation:
You want the y-coordinate of point C on the line x=-3 so that ∆ABC has area 6 square units with segment AB being 6 units long.
Area
The formula for the area of a triangle is ...
A = 1/2bh
Given the base of 6 units, and area of 6 square units, we find the height to be ...
6 = 1/2(6)h
6/3 = h = 2
The height of the triangle is 2 units.
Coordinates
Point C is given as being on the line x=-3. Its y-coordinate must differ from the y-coordinates of A and B by 2 units. Those y-coordinates are 2, so the y-coordinate of C is ...
2 ±2 = {4, 0}
Point C may have a y-coordinate of 0 or 4. The appropriate answer choice is 4.
