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Given a triangle bounded by the lines 2x + y - 10 = 0, x + 5 =

0, and y + 4 = 0.
Find the equations (in general form) of the following. Also, find
the coordinates of their respective point of concurre

User Gillardo
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1 Answer

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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.

  1. For the equation 2x + y - 10 = 0, we subtract 2x and y from both sides to get -2x - y + 10 = 0.
  2. For the equation x + 5 = 0, we subtract x from both sides to get -x + 5 = 0.
  3. 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).

User Edwin Dalorzo
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