Module 1- Geometric Reasoning Review

Front

What is the formula for finding the weighted average of two points A and B with weights?

Back

Weighted Average = (w1 * A + w2 * B) / (w1 + w2), where w1 and w2 are the weights of points A and B.

Front

How do you find the coordinates of a point P that divides a line segment AB in a given ratio?

Back

Use the section formula: P(x,y) = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)), where m:n is the ratio and A(x1,y1), B(x2,y2).

Front

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

Back

Midpoint M = ((x1 + x2)/2, (y1 + y2)/2).

Front

Define coplanar points.

Back

Coplanar points are points that lie on the same plane.

Front

How many points are needed to define a plane?

Back

Three non-collinear points are needed to define a plane.

Front

What is the definition of a line segment?

Back

A line segment is a part of a line that is bounded by two distinct endpoints.

Front

What is the distance formula between two points (x1, y1) and (x2, y2)?

Back

Distance = √((x2 - x1)² + (y2 - y1)²).

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

What is the significance of the x-coordinate and y-coordinate in a point (x, y)?

Back

The x-coordinate indicates the horizontal position, while the y-coordinate indicates the vertical position of the point in the coordinate plane.

Front

How do you determine if three points are collinear?

Back

Three points are collinear if the area of the triangle formed by them is zero, which can be checked using the determinant method.