How can I prove a line is an altitude

To prove that a line is an altitude, you need to show that it is perpendicular to the base of the triangle and passes through the opposite vertex. Here's how you can prove it:

1. Identify the triangle: Determine the triangle for which you want to prove the line is an altitude.

2. Identify the base: Identify the side of the triangle on which you suspect the altitude lies.

3. Check for perpendicularity: Use the slope formula to calculate the slopes of the base and the given line. If the slopes are negative reciprocals (their product is -1), then the line is perpendicular to the base.

4. Check for containment: Determine if the line passes through the opposite vertex of the triangle. You can do this by substituting the coordinates of the opposite vertex into the equation of the line. If the equation is satisfied, then the line passes through the vertex.

By proving both perpendicularity and containment, you can establish that the line is indeed an altitude of the triangle you are considering.