Altitude and Slope in Triangles

Anil Kumar explains how to find the equation of the altitude from a vertex of a triangle in coordinate geometry. The process involves sketching the triangle, calculating the slope of a line segment, and using the negative reciprocal to find the slope of the altitude. The final equation is derived using the point-slope form. Emphasis is placed on the importance of detailed steps to avoid losing marks.

Why is it important to avoid mistakes in exams, according to the introduction?

• They can result in losing a few marks.

• They can be easily corrected later.

• They can lead to a complete failure.

• They are not significant in the overall score.

What is the main task in the problem statement?

• Finding the area of a triangle.

• Identifying the type of triangle.

• Determining the equation of an altitude.

• Calculating the perimeter of a triangle.

What is the first step in solving the problem?

• Calculating the area.

• Measuring the angles.

• Sketching the triangle.

• Finding the midpoint.

What does the altitude of a triangle represent?

• A line parallel to the base.

• A line dividing the triangle into two equal areas.

• A line bisecting the angle.

• A perpendicular from a vertex to the opposite side.

How is the slope of line segment BC calculated?

• Using the distance formula.

• By measuring the angle with the x-axis.

• Using the formula y2 - y1 / x2 - x1.

• By finding the midpoint of BC.

What is the slope of the altitude AD?

• Twice the slope of BC.

• The negative reciprocal of the slope of BC.

• Half the slope of BC.

• The same as the slope of BC.

Which point is used to find the equation of the altitude?

• Point D

• Point B

• Point C

• Point A

What is the y-intercept of the altitude's equation?

• 4

• 6

• 18

• 12

What is the final equation of the altitude?

• y = -4x + 18

• y = 4x + 18

• y = -4x + 12

• y = 4x - 18

Why is it important to write down all steps in calculations?

• To make the solution longer.

• To ensure full marks are awarded.

• To confuse the examiner.

• To avoid any mistakes.