Ch. 4 Coordinate Proofs

Front

What is the midpoint of a line segment?

Back

The midpoint of a line segment is the point that divides the segment into two equal parts. It can be found using the formula: Midpoint M = ((x1 + x2)/2, (y1 + y2)/2) where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

Front

How do you find the slope of a line?

Back

The slope of a line is calculated as the change in y divided by the change in x (rise over run). The formula is: Slope (m) = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points on the line.

Front

What is a coordinate proof?

Back

A coordinate proof is a method of proving geometric theorems using algebra and the coordinate plane. It involves placing geometric figures on a coordinate grid and using algebraic techniques to demonstrate properties.

Front

What are the coordinates of the midpoint between (2, 3) and (4, 7)?

Back

The midpoint is ((2 + 4)/2, (3 + 7)/2) = (3, 5).

Front

What is the formula for the distance between two points?

Back

The distance d between two points (x1, y1) and (x2, y2) is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

How do you determine if two lines are parallel using slopes?

Back

Two lines are parallel if they have the same slope. If the slopes (m1 and m2) of two lines are equal (m1 = m2), then the lines are parallel.

Front

What is the significance of the slope in a coordinate plane?

Back

The slope indicates the steepness and direction of a line. A positive slope means the line rises from left to right, while a negative slope means it falls.

Front

What is the formula for the slope of a line given two points?

Back

The formula for the slope (m) of a line given two points (x1, y1) and (x2, y2) is: m = (y2 - y1) / (x2 - x1).

Front

How can you find the length of a diagonal in a rectangle?

Back

The length of a diagonal in a rectangle can be found using the Pythagorean theorem: d = √(length² + width²).

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of two perpendicular lines are negative reciprocals of each other. If one line has a slope of m, the other will have a slope of -1/m.