Finding the Line of Symmetry for an Isosceles Triangle - Algebraic Solution

The video tutorial guides students through solving a geometry problem involving an isosceles triangle. It explains how to rearrange a line equation, visualize the triangle, calculate the perpendicular gradient, and derive the equation for the line of symmetry. The tutorial emphasizes a step-by-step approach and concludes with a marking scheme and advice for practice.

What is the significance of the coordinates of point A in the problem?

• They determine the length of line BC.

• They help in finding the line of symmetry.

• They are used to calculate the area of the triangle.

• They are irrelevant to the problem.

What is the first step in rearranging the equation of line BC?

• Multiply the entire equation by 3.

• Divide the entire equation by 3.

• Subtract 12 from both sides.

• Add 12 to both sides.

Why is it important to rearrange the equation into the form y = mx + c?

• To convert it into a quadratic equation.

• To find the y-intercept of the line.

• To determine the slope of the line.

• To simplify the equation for easier calculations.

What characteristic of the line of symmetry is crucial for solving the problem?

• It is shorter than line BC.

• It is longer than line BC.

• It is parallel to line BC.

• It is perpendicular to line BC.

How do you find the gradient of the line of symmetry?

• By taking the reciprocal of the gradient of line BC.

• By doubling the gradient of line BC.

• By halving the gradient of line BC.

• By taking the negative reciprocal of the gradient of line BC.

What is the value of C in the equation of the line of symmetry?

• 37

• 43

• 86

• 12

Why do we multiply the equation by 2 in the final steps?

• To adjust the y-intercept.

• To change the slope of the line.

• To make the equation more complex.

• To eliminate fractions and have integer coefficients.

What is the final form of the equation for the line of symmetry?

• 2x - 3y = 86

• 3x - 2y = 86

• 2x + 3y = 86

• 3x + 2y = 86

What is the purpose of rearranging the equation into the form PX + QY = R?

• To simplify the equation for graphing.

• To ensure all coefficients are integers.

• To find the intersection points.

• To convert it into a quadratic equation.

What is the key takeaway from solving this problem?

• Understanding the properties of isosceles triangles.

• Practicing the step-by-step approach to problem-solving.

• Mastering the use of the quadratic formula.

• Learning to solve equations with multiple variables.