Understanding Slopes and Triangles

The video tutorial explains how to find the equations of the sides of an isosceles right triangle given the equation of the hypotenuse and a vertex point. It covers calculating the slope of line BC, deriving its equation using the point-slope form, and then finding the equation of line AB by using the negative reciprocal of the slope of BC. The session concludes with a summary of the process.

What type of triangle is discussed in the video?

• Obtuse triangle

• Scalene triangle

• Isosceles right triangle

• Equilateral triangle

What is the angle between the two equal sides of the triangle?

• 30°

• 90°

• 60°

• 45°

What is the equation of the hypotenuse given in the problem?

• 3x + 4y = 4

• 2x + 3y = 5

• x + y = 1

• 4x + 3y = 7

What is the given vertex opposite the hypotenuse?

• (3, 3)

• (2, 2)

• (4, 4)

• (1, 1)

How do you find the slope of a line from its equation?

• By dividing the x-coefficient by the y-coefficient

• By adding the coefficients of x and y

• By taking the negative reciprocal of the y-intercept

• By rearranging the equation to y = mx + c form

What is the slope of the line BC derived from the hypotenuse equation?

• -7

• -3/4

• 4/3

• 1/7

What is the relationship between the slopes of perpendicular lines?

• They are equal

• They are negative reciprocals

• They are both zero

• They are both positive

What is the slope of line AB if BC's slope is 1/7?

• 7

• -7

• 1/7

• -1/7

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

• Slope-intercept form

• Point-slope form

• Intercept form

• Standard form

What is the equation of line BC derived in the video?

• x + 7y - 12 = 0

• x + y = 0

• x - 7y + 12 = 0

• 7x + y - 16 = 0