Determine whether each statement is true or false. If false, explain why. The midpoint of the segment joining (0, 0) and (4, 4) is 2.

Verified step by step guidance

1. <insert step 1> Calculate the midpoint of a line segment using the midpoint formula: \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \).>
2. <insert step 2> Substitute the given points (0, 0) and (4, 4) into the formula: \( M = \left( \frac{0 + 4}{2}, \frac{0 + 4}{2} \right) \).>
3. <insert step 3> Simplify the expressions inside the parentheses: \( M = \left( \frac{4}{2}, \frac{4}{2} \right) \).>
4. <insert step 4> Further simplify to find the coordinates of the midpoint: \( M = (2, 2) \).>
5. <insert step 5> Conclude that the statement is false because the midpoint is a point with coordinates (2, 2), not a single number like 2.>

Key Concepts

Midpoint Formula

The midpoint of a line segment in a coordinate plane is calculated using the midpoint formula, which is given by M = ((x1 + x2)/2, (y1 + y2)/2). This formula averages the x-coordinates and the y-coordinates of the endpoints to find the point that is exactly halfway between them.

Coordinates of Points

Coordinates are pairs of numbers that define the position of a point in a two-dimensional space. In this case, the points (0, 0) and (4, 4) represent specific locations on the Cartesian plane, where the first number is the x-coordinate and the second is the y-coordinate.

True or False Statements

In mathematics, determining whether a statement is true or false involves verifying its accuracy based on established definitions and properties. If a statement is false, it is important to provide a clear explanation of why it does not hold true, often by demonstrating the correct reasoning or calculation.