Finding the Orthocenter of a Triangle

What is the first step in finding the orthocenter of a triangle using coordinate geometry?

• Plot the vertices on a coordinate plane

• Determine the length of each side

• Calculate the area of the triangle

• Find the centroid of the triangle

What is the equation of a vertical line that serves as an altitude in a triangle?

• y = a constant

• y = mx + b

• x = y

• x = a constant

How do you determine the slope of a line perpendicular to a given line with slope -1?

• Keep the slope the same

• Use the reciprocal, which is 1

• Use the negative reciprocal, which is 1

• Use the negative reciprocal, which is -1

What is the y-intercept of the altitude through point A if the slope is 1 and it passes through (-3, 3)?

• 0

• 3

• 9

• 6

What is the slope of a line perpendicular to a line with slope 2?

• 2

• -2

• -1/2

• 1/2

Which form of the equation is used to find the altitude through point C?

• Slope-intercept form

• Standard form

• Quadratic form

• Point-slope form

What is the orthocenter of triangle ABC if the altitudes intersect at (-1, 5)?

• (-1, 5)

• (0, 0)

• (5, -1)

• (1, -5)

How can you verify the orthocenter using the equations of the altitudes?

• By calculating the area of the triangle

• By finding the midpoint of the triangle

• By checking if the point lies on all three altitudes

• By measuring the angles of the triangle

What is the result of solving the system of equations for the altitudes of triangle ABC?

• The incenter of the triangle

• The centroid of the triangle

• The orthocenter of the triangle

• The circumcenter of the triangle

What is the significance of the point where the altitudes intersect in a triangle?

• It is the orthocenter

• It is the incenter

• It is the circumcenter

• It is the centroid