Semester Review - Module 1

Front

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

Back

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

Front

What is the midpoint between the points (3, -1) and (7, -5)?

Back

(5, -3)

Front

If point A is at (-4, 2) and the midpoint M is at (8, 7), how do you find the other endpoint B?

Back

Use the formula B = (2M - A). In this case, B = (2(8, 7) - (-4, 2)) = (20, 12).

Front

What is a weighted average?

Back

A weighted average is an average that takes into account the relative importance of each value. It is calculated by multiplying each value by its weight, summing these products, and then dividing by the total weight.

Front

Calculate the weighted average of points A (-3) and B (9) with weights 2 and 3 respectively.

Back

The weighted average P = (2 * -3 + 3 * 9) / (2 + 3) = 4.2.

Front

What does it mean for a point to be the midpoint of a segment?

Back

A midpoint divides a segment into two equal parts, meaning the distances from the midpoint to each endpoint are the same.

Front

If R is the midpoint of segment QS, how do you find the length of segment QS?

Back

The length of segment QS is twice the distance from R to either endpoint.

Front

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

Back

The distance d is given by d = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Front

How do you find the coordinates of a midpoint given two endpoints?

Back

Add the x-coordinates of the endpoints and divide by 2 for the x-coordinate of the midpoint, and do the same for the y-coordinates.

Front

What is the significance of the coordinates of a midpoint in geometry?

Back

The coordinates of a midpoint represent the average position of two points in a coordinate plane.