Coordinate Geometry

Front

What is the midpoint formula for two points (x1, y1) and (x2, y2)?

Back

The midpoint M is given by M = ((x1 + x2)/2, (y1 + y2)/2).

Front

How do you calculate the distance between two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the Pythagorean theorem?

Back

In a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c² = a² + b².

Front

What is the opposite operation of squaring a number?

Back

The opposite operation of squaring a number is taking the square root.

Front

If a right triangle has sides of lengths 6, 8, and 10, which side is the hypotenuse?

Back

The hypotenuse is the longest side, which is 10.

Front

What is the formula for the area of a triangle?

Back

The area A of a triangle is given by A = (1/2) * base * height.

Front

What is the definition of a coordinate plane?

Back

A coordinate plane is a two-dimensional surface formed by the intersection of a horizontal line (x-axis) and a vertical line (y-axis).

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.