Understanding Altitudes and Gradients in Triangles

The video tutorial explains the concept of altitudes in triangles, highlighting the difference between altitudes and medians. It provides a step-by-step guide on calculating the equation of an altitude using the gradient formula and demonstrates this with examples of altitudes CE and BF. The tutorial emphasizes the importance of understanding perpendicular lines and gradients in analytical geometry.

What is a vertex in the context of a triangle?

• An angle bisector

• The midpoint of a side

• A corner of the triangle

• A line segment

What is the key characteristic of an altitude in a triangle?

• It is parallel to the base

• It forms a 90-degree angle with the opposite side

• It is the longest side of the triangle

• It bisects the opposite side

How does an altitude differ from a median in a triangle?

• A median forms a 90-degree angle with the opposite side

• An altitude is always the longest line

• A median goes to the midpoint of the opposite side

• An altitude is parallel to the base

What is the first step in determining the equation of an altitude?

• Identify the longest side of the triangle

• Draw a perpendicular line from the vertex

• Calculate the gradient of the opposite side

• Find the midpoint of the opposite side

In the example of altitude CE, what is the gradient of line AB?

• 1/2

• -3/5

• -4/3

• 3/4

What is the equation of line CE in the example provided?

• y = -4/3x + 1

• y = 3/4x - 1/2

• y = -3/5x + 7/5

• y = 3/4x + 1/2

In the example of altitude BF, what is the gradient of line AC?

• -4/3

• 4/3

• -3/5

• 5/3

What is the equation of line BF in the example provided?

• y = -4/3x + 1

• y = 3/4x - 1/2

• y = -3/5x + 7/5

• y = 5/3x + 1