Altitude and Slope in Triangles

The video tutorial explains how to find the equation of an altitude from a vertex in a triangle. It begins by introducing the concept of altitude and the importance of identifying the vertex. The instructor then demonstrates how to draw the triangle and label the vertices. The process of finding the slope of the line and its negative reciprocal is explained, followed by deriving the equation of the altitude using the slope and a known point on the line.

What is the first step in finding the equation of an altitude from a vertex in a triangle?

• Identify the vertex and opposite side

• Calculate the area of the triangle

• Determine the type of triangle

• Find the midpoint of the base

When labeling a triangle for altitude calculation, where should the vertex be placed?

• At the bottom

• At the top

• On the left side

• On the right side

What is the characteristic of the altitude in a triangle?

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

• It is the longest side of the triangle

• It is parallel to the base

• It bisects the opposite side

How do you find the slope of the line opposite the vertex?

• By using the Pythagorean theorem

• By finding the midpoint

• By measuring the angle

• By using the formula y2 - y1 over x2 - x1

What is the slope of the line opposite the vertex if the coordinates are (x1, y1) and (x2, y2)?

• (x1 - x2) / (y1 - y2)

• (y1 - y2) / (x1 - x2)

• (y2 - y1) / (x2 - x1)

• (x2 - x1) / (y2 - y1)

What is the next step after finding the slope of the opposite line?

• Determine the length of the altitude

• Calculate the area of the triangle

• Find the negative reciprocal of the slope

• Draw a perpendicular bisector

What is the negative reciprocal of a slope of 5/7?

• -5/7

• 7/5

• 5/7

• -7/5

What is the purpose of finding the negative reciprocal of a slope?

• To calculate the area of the triangle

• To determine the perpendicular slope

• To find the midpoint of the base

• To find the length of the altitude

Which form is used to find the equation of the altitude line?

• Point-slope form

• Standard form

• Quadratic form

• Slope-intercept form

What is the only point that can be substituted into the altitude equation?

• The vertex from which the altitude is drawn

• The midpoint of the base

• The centroid of the triangle

• Any point on the base