Understanding the Orthocenter of a Triangle

The video tutorial explains how to find the orthocenter of a triangle, which is the point where the three altitudes intersect. It covers the process of calculating slopes, finding perpendicular slopes, deriving equations of lines, and determining the intersection point algebraically. The tutorial uses a step-by-step approach to demonstrate these concepts, ensuring a clear understanding of how to locate the orthocenter in a triangle.

What is the orthocenter of a triangle?

• The point where the angle bisectors intersect

• The point where the altitudes intersect

• The point where the medians intersect

• The point where the perpendicular bisectors intersect

What is the first step in finding the perpendicular slope of a line?

• Square the slope

• Add the slopes of two lines

• Multiply the slopes of two lines

• Find the reciprocal of the slope and change its sign

If a line has a slope of -3, what is the slope of a line perpendicular to it?

• 1/3

• -1/3

• 3

• -3

Which form is used to derive the equation of a line given a point and a slope?

• Slope-intercept form

• Point-slope form

• Standard form

• Quadratic form

What is the equation of a line with a slope of 1 passing through the point (0,1)?

• y = -x + 1

• y = x + 1

• y = x - 1

• y = -x - 1

How do you find the point of intersection of two lines?

• By multiplying their equations

• By adding their equations

• By setting their equations equal to each other

• By subtracting their equations

What is the x-coordinate of the intersection point of the lines y = x + 1 and y = -5x + 15?

• 5

• 2

• 3

• 7/3

What is the y-coordinate of the intersection point of the lines y = x + 1 and y = -5x + 15?

• 7/3

• 10/3

• 5

• 3

Why is it important to verify the calculated orthocenter?

• To ensure the diagram is aesthetically pleasing

• To determine the type of triangle

• To confirm the accuracy of the calculations

• To check if the triangle is equilateral

What does the orthocenter represent in the context of a triangle?

• The center of the circle inscribed in the triangle

• The midpoint of the triangle's base

• The highest point of the triangle

• The intersection of the triangle's altitudes