Дан треугольник с вершинами в точках A(1;1), B(8;2), С(7;9). Задайте уравнением прямую BC. Задайте уравнением прямую, содержащую высоту BH этого треугольника. В поле ввода введите целое число или десятичную дробь.
The equation of line BC is y = (1/7)x + 14/7.
The equation of the line containing the height BH of this triangle is y = -7x + 11. Keep in mind that the height BH is perpendicular to the base BC and passes through the point B. Hence, the slope of the height BH is the negative reciprocal of the slope of the base BC.
To find the slope of the base BC, use the slope formula (𝑦2−𝑦1/𝑥2−𝑥1) with the points B(8,2) and C(7,9).
(9-2)/(7-8) = -7
Since the slope of the base BC is -7, the slope of the height BH would be the negative reciprocal, which is 1/7.
To find the y-intercept of the height BH, substitute the coordinates of point B into the equation y = mx + b and solve for b.
2 = (1/7)*8 + b
b = 14/7
Hence, the equation of the line containing the height BH is y = (1/7)x + 14/7.
For the final step, input the desired value for x into the equation of the height BH to find the corresponding y-value. Remember, x corresponds to the x-coordinate of the point on the base BC, while y corresponds to the distance from that point to the height BH.
