Exploring Coordinate Proofs and Perpendicular Segments

This video tutorial introduces coordinate proofs, focusing on proving special values on the coordinate plane. It covers positioning and labeling right triangle XYZ, identifying missing coordinates of isosceles right triangle QRS, and exploring properties of a general isosceles triangle. The tutorial concludes with a demonstration of proving perpendicularity using slopes in coordinate geometry.

What is the primary focus of coordinate proofs?

• Drawing complex shapes

• Calculating areas of polygons

• Finding the shortest path between points

• Proving special values on the coordinate plane

In the first example of positioning a right triangle, what are the coordinates of point Z if leg XZ is d units long?

• (0, 0)

• (d, d)

• (0, d)

• (d, 0)

In the second example of positioning a right triangle, what are the coordinates of point Z if leg XZ is d units long?

• (d, 0)

• (-d, 0)

• (0, d)

• (0, -d)

For an isosceles right triangle with Q at (0, 0) and R at (a, 0), what are the coordinates of point S?

• (a, a)

• (0, 0)

• (a, 0)

• (0, a)

If an isosceles triangle has a point at (-a, 0), where is the corresponding point on the x-axis?

• (0, a)

• (a, 0)

• (-a, a)

• (0, 0)

In an isosceles triangle, if one point is at (3a, 0), where is the midpoint of the base?

• (1.5a, 0)

• (1.5a, b)

• (3a, 0)

• (0, 1.5a)

What is the goal of the coordinate proof involving the segment joining the vertex angle of an isosceles triangle to the midpoint of its base?

• To prove the segment is parallel to the base

• To prove the segment is perpendicular to the base

• To find the length of the segment

• To calculate the area of the triangle

What is the slope of a line that is perpendicular to a line with an undefined slope?

• Positive

• Zero

• Undefined

• Negative

If the slope of line YW is undefined, what is the slope of line XZ?

• Negative

• Positive

• Undefined

• Zero

What does it mean if two lines have slopes that are negative reciprocals of each other?

• They are parallel

• They are perpendicular

• They intersect at an acute angle

• They do not intersect