Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them. A(-6, 3), B(-6,8)

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Identify the coordinates of the two points: A(-6, 3) and B(-6, 8).

Use the distance formula to find the distance between points A and B: \(\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of points A and B respectively.

Substitute the coordinates into the distance formula: \(\sqrt{(-6 - (-6))^2 + (8 - 3)^2}\).

Use the midpoint formula to find the midpoint coordinates: \(\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)\).

Substitute the coordinates into the midpoint formula: \(\left( \frac{-6 + (-6)}{2}, \frac{3 + 8}{2} \right)\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Distance Formula

The distance formula calculates the length between two points in the coordinate plane. It is derived from the Pythagorean theorem and given by d = √[(x2 - x1)² + (y2 - y1)²], where (x1, y1) and (x2, y2) are the coordinates of the points.

Midpoint Formula

The midpoint formula finds the point exactly halfway between two given points. It is calculated as ((x1 + x2)/2, (y1 + y2)/2), providing the average of the x-coordinates and y-coordinates of the endpoints.

Coordinate Geometry Basics

Understanding the Cartesian coordinate system is essential, where points are represented as (x, y). This knowledge helps in visualizing points, line segments, and applying formulas like distance and midpoint effectively.