Distance, Midpoint, Area & Perimeter on the Coordinate Plane

Front

What is the formula for the area of a triangle on the coordinate plane?

Back

The area of a triangle can be calculated using the formula: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \) or using the coordinates of the vertices: \( \text{Area} = \frac{1}{2} | x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) | \).

Front

What is the formula for the perimeter of a triangle given its vertices?

Back

The perimeter of a triangle can be calculated by summing the lengths of its sides: \( P = d(A, B) + d(B, C) + d(C, A) \), where \( d \) is the distance formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Front

How do you find the distance between two points (x1, y1) and (x2, y2) on the coordinate plane?

Back

The distance between two points is given by the formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Front

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

Back

The midpoint M of the line segment connecting two points is given by: \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \).

Front

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

Back

If two lines have slopes that are negative reciprocals, they are perpendicular to each other.

Front

What is the area of a rectangle given its length and width?

Back

The area of a rectangle is calculated using the formula: \( \text{Area} = \text{length} \times \text{width} \).

Front

How do you calculate the perimeter of a rectangle?

Back

The perimeter of a rectangle is calculated using the formula: \( P = 2 \times (\text{length} + \text{width}) \).

Front

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

Back

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

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope.

Front

What is the formula for the area of a triangle given its vertices (x1, y1), (x2, y2), (x3, y3)?

Back

The area can be calculated using: \( \text{Area} = \frac{1}{2} | x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) | \).