Review B.9, B.10 and B.13

Front

What is the definition of coordinates in a Cartesian plane?

Back

Coordinates are a set of values that show an exact position. In a 2D Cartesian plane, a point is represented by an ordered pair (x, y), where 'x' is the horizontal distance from the origin and 'y' is the vertical distance.

Front

How do you find the midpoint of a line segment between two points (x1, y1) and (x2, y2)?

Back

The midpoint M is calculated using the formula M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the distance formula used to find the length of a line segment between two points (x1, y1) and (x2, y2)?

Back

The distance d is calculated using the formula d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the significance of the origin in a Cartesian coordinate system?

Back

The origin is the point (0, 0) where the x-axis and y-axis intersect. It serves as the reference point for measuring coordinates.

Front

How do you determine if a point lies on a given line?

Back

A point (x, y) lies on a line if it satisfies the equation of the line when the coordinates are substituted into the equation.

Front

What is the formula for calculating the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two lines to be parallel in terms of their slopes?

Back

Two lines are parallel if they have the same slope, meaning they rise and run at the same rate and never intersect.

Front

What is the formula for the area of a triangle given its base and height?

Back

The area A is calculated using the formula A = (1/2) * base * height.

Front

How do you find the coordinates of the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3)?

Back

The centroid G is found using the formula G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

Front

What is the relationship between the lengths of the sides of a right triangle?

Back

In a right triangle, the lengths of the sides satisfy the Pythagorean theorem: a² + b² = c², where c is the length of the hypotenuse.