Midpoint and Distance Formula

Front

What is the Midpoint Formula?

Back

The Midpoint Formula is used to find the midpoint (M) between two points (x1, y1) and (x2, y2) in a coordinate plane: M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the Distance Formula?

Back

The Distance Formula calculates the distance (d) between two points (x1, y1) and (x2, y2): d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect, and it is equidistant from all three vertices.

Front

How do you find the other endpoint if you have one endpoint and the midpoint?

Back

Use the formula: Other Endpoint = (2 * Midpoint) - Endpoint.

Front

What is the slope of a line?

Back

The slope (m) of a line is a measure of its steepness, calculated as m = (y2 - y1) / (x2 - x1).

Front

What does it mean for a point to be equidistant from two other points?

Back

A point is equidistant from two other points if it is the same distance from both points.

Front

What is the significance of the circumcenter in a right triangle?

Back

In a right triangle, the circumcenter is located at the midpoint of the hypotenuse.

Front

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

Back

Substitute the point's coordinates into the line's equation; if the equation holds true, the point lies on the line.

Front

What is the formula for finding the slope of a line passing through two points?

Back

The formula is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the relationship between the circumcenter and the vertices of a triangle?

Back

The circumcenter is equidistant from all three vertices of the triangle.