The vertices of triangle ABC are given: A (0; 2), B (12; -7) and C (16; 15). Write down the equations of its sides.
June 11, 2021 | education
| The equation is y = k * x + b. Substitute the values of the coordinates of the points in the function formula and get the equation of the straight line.
1) A (0; 2), B (12; -7).
2 = 0 * k + b;
-7 = 12 * k + b;
b = 2;
-7 = 12 * k + 2;
12 * k = -9;
k = -3/4;
We get the equation of the straight line:
y = -3/4 * x + 2.
2) A (0; 2), C (16; 15).
2 = 0 * k + b;
15 = 16 * k + b;
b = 2;
15 = 16 * k + 2;
16 * k = 13;
k = 13/16;
We get the equation of the straight line:
y = 13/16 * x + 2.
3) B (12; -7), C (16; 15).
-7 = 12 * k + b;
15 = 16 * k + b;
Subtract the first from the second equation by the Gauss method:
16 * k – 12 * k = 15 + 7;
4 * k = 22;
k = 11/2;
b = 15 – 16 * 11/2 = 15 – 88 = -73;
We get the equation of the straight line:
y = 11/2 * x – 73.
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