The midpoint and distance formulas are useful tools for solving problems in geometry. These formulas enable you to find the midpoint of a line segment, the distance between two points, and the coordinates of a point that lies a certain distance from another point. By combining these formulas, you can find the answers to a variety of geometry problems.

## The Midpoint Formula

The midpoint formula is used to find the midpoint of a line segment. The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the line segment. The formula for the midpoint isM = (x1 + x2)/2, (y1 + y2)/2where M is the midpoint, (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment. To use this formula, you simply plug in the coordinates of the endpoints of the line segment and solve for M.

## The Distance Formula

The distance formula is used to find the distance between two points. The formula for the distance isd = √ (x2 – x1)2 + (y2 – y1)2where d is the distance, (x1, y1) and (x2, y2) are the coordinates of the two points. To use this formula, you simply plug in the coordinates of the two points and solve for d.

## Combining the Formulas

By combining the midpoint and distance formulas, you can solve a variety of geometry problems. For example, you can use these formulas to find the coordinates of a point that lies a certain distance from another point. To do this, you first calculate the midpoint of the two points using the midpoint formula. Then, you use the distance formula to calculate the distance between the two points. Finally, you use the distance formula again to calculate the coordinates of the point that lies a certain distance from the midpoint.

The midpoint and distance formulas are useful tools for solving geometry problems. By combining these formulas, you can find the answers to a variety of questions involving midpoints, distances, and points that lie a certain distance from each other. With a bit of practice, you can become proficient in using these formulas to find the answers to your geometry questions.

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