The vertices of the ABC triangle have coordinates A (-7; 5) B (3; -1) C (5; 3). Make the equations of lines AB, BC, CA.

| September 28, 2021 | education

To compose the equations of straight lines, there is a formula:
(x – x1) / (x2 – x1) = (y – y1) / (y2 – y1). Where x1 and x2 are the coordinates of the first point, and y1 and y2 are the second.
We compose the equation of the straight line AB:
(x – (- 7)) / (5 – (- 7)) = (y – 3) / (- 1 – 3),
(x + 7) / (5 + 7) = (y – 3) / (- 4),
(x + 7) / 12 = (y – 3) / (- 4),
– 4 (x + 7) = 12 (y – 3),
– 4x – 28 = 12y – 36,
– 12y – 4x – 28 + 36 = 0,
– 12y – 4x + 8 = 0,
4x + 12y – 8 = 0.
Answer: the equation of the straight line AB: 4x + 12y – 8 = 0.
We compose the equation of the straight line BC:
(x – 3) / (- 1 – 3) = (y – 5) / (3 – 5),
(x – 3) / (- 4) = (y – 5) / (- 2),
– 2 (x – 3) = – 4 (y – 5),
– 2x + 6 = – 4y + 20,
4y – 2x + 6 – 20 = 0,
4y – 2x – 14 = 0,
2x – 4y + 14 = 0.
Answer: the equation of the straight line BC: 2x – 4y + 14 = 0.
We compose the equation of the straight line SA:
(x – 5) / (3 – 5) = (y – (- 7)) / (5 – (- 7)),
(x – 5) / (- 2) = (y + 7) / 12,
12 (x – 5) = – 2 (y + 7),
12x – 60 = – 2y – 14,
12x + 2y – 60 + 14 = 0,
12x + 2y – 46 = 0.
Answer: the equation of the straight line CA: 12x + 2y – 46 = 0.



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