Question

In a triangle ABC with vertices A(2,3), B(4, -1), and C(1,2), find the equation and length of the altitude from vertex A.

a) Equation of altitude: 4x - 3y + 10 = 0, Length = √13
b) Equation of altitude: 2x - y + 5 = 0, Length = √13
c) Equation of altitude: x - 2y + 3 = 0, Length = √10
d) Equation of altitude: 3x - 4y + 12 = 0, Length = √10

Answer 1

To find the equation and length of the altitude from vertex A in the triangle ABC, follow these steps: Find the slope of the line passing through points B and C. Using the slope, find the equation of the line passing through point A. Find the intersection point of the two lines to get the foot of the altitude.

Step-by-step explanation:

To find the equation and length of the altitude from vertex A in the triangle ABC, we can follow these steps:

1. Find the slope of the line passing through points B and C.
2. Using the slope, find the equation of the line passing through point A.
3. Find the intersection point of the two lines to get the foot of the altitude.
4. Calculate the distance between the foot of the altitude and point A to find the length of the altitude.

The correct option is a) Equation of altitude: 4x - 3y + 10 = 0, Length = √13.