Final answer:
To show that the points A(3,4), B(3,1), and C(8,4) form a right triangle, we can use the distance formula. The length of the perpendicular from A to BC can be calculated using the formula: Length of perpendicular = |m * (x2 - x1) - (y2 - y1) + y1| / sqrt(m^2 + 1)
Step-by-step explanation:
To show that the points A(3,4), B(3,1), and C(8,4) form a right triangle, we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can calculate the distances AB, AC, and BC, and then check if the Pythagorean theorem (a^2 + b^2 = c^2) is true for these distances. If it is, then the points form a right triangle.
The length of the perpendicular from A to BC can be calculated using the formula:
Length of perpendicular = |m * (x2 - x1) - (y2 - y1) + y1| / sqrt(m^2 + 1)
where m is the slope of BC.