Coordinate Geometry

Front

What is the distance formula in coordinate geometry?

Back

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

Front

How do you find the midpoint of a line segment?

Back

The midpoint M of a segment with endpoints (x1, y1) and (x2, y2) is given by: \(M = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)\).

Front

What is the area of a rectangle?

Back

The area A of a rectangle is calculated using the formula: \(A = length \times width\).

Front

What is the perimeter of a rectangle?

Back

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

Front

How do you calculate the area of a polygon given its vertices?

Back

To find the area of a polygon with vertices, use the shoelace formula or divide the polygon into triangles and sum their areas.

Front

What is the formula for the area of a triangle?

Back

The area A of a triangle is given by: \(A = \frac{1}{2} \times base \times height\).

Front

What is the significance of the coordinates in coordinate geometry?

Back

Coordinates represent points in a plane, defined by an ordered pair (x, y), where x is the horizontal position and y is the vertical position.

Front

How do you determine if three points are collinear?

Back

Three points (x1, y1), (x2, y2), (x3, y3) are collinear if the area of the triangle they form is zero, which can be checked using the determinant method.

Front

What is the slope of a line?

Back

The slope m of a line through two points (x1, y1) and (x2, y2) is given by: \(m = \frac{y2 - y1}{x2 - x1}\).

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is: \(y = mx + b\), where m is the slope and b is the y-intercept.