Final answer:
To find the equations of the lines in general form, we first need to convert the given equations to the general form of a line. The equations in general form are -2x - y + 10 = 0, -x + 5 = 0, and 4 - y = 0. The coordinates of their respective point of concurrency are (5, 4) and (-10, 4).
Step-by-step explanation:
The given triangle is bounded by the lines 2x + y - 10 = 0, x + 5 = 0, and y + 4 = 0. To find the equations of the lines in general form, we first need to convert the given equations to the general form of a line: Ax + By + C = 0.
- For the equation 2x + y - 10 = 0, we subtract 2x and y from both sides to get -2x - y + 10 = 0.
- For the equation x + 5 = 0, we subtract x from both sides to get -x + 5 = 0.
- For the equation y + 4 = 0, we subtract y from both sides to get 4 - y = 0.
Therefore, the equations in general form are -2x - y + 10 = 0, -x + 5 = 0, and 4 - y = 0. To find the coordinates of their respective point of concurrency, we can solve two pairs of equations to find the intersection points. By solving -x + 5 = 0 and 4 - y = 0, we get x = 5 and y = 4. Thus, the first point of concurrency is (5, 4). Similarly, by solving -2x - y + 10 = 0 and 4 - y = 0, we get x = -10 and y = 4. Therefore, the second point of concurrency is (-10, 4).