A Square Is Drawn On A Coordinate Grid So That Two Diagonally Oppostite Vertices Of The Square Have Coordinates (-2,9) And (5,2)
Introduction
In mathematics, a coordinate grid is a system of two perpendicular lines that intersect at a point called the origin. The x-axis and y-axis are the two perpendicular lines that form the coordinate grid. The x-axis is horizontal and the y-axis is vertical. The point where the x-axis and y-axis intersect is called the origin, and it is denoted by the coordinates (0, 0). In this article, we will explore the concept of a square drawn on a coordinate grid, with two diagonally opposite vertices having coordinates (-2, 9) and (5, 2).
What is a Square?
A square is a four-sided shape with four right angles and four equal sides. It is a type of quadrilateral, which is a polygon with four sides. The opposite sides of a square are parallel and equal in length. The diagonals of a square bisect each other at right angles. In other words, the diagonals of a square intersect at their midpoints and form right angles.
Understanding the Coordinate Grid
A coordinate grid is a system of two perpendicular lines that intersect at a point called the origin. The x-axis and y-axis are the two perpendicular lines that form the coordinate grid. The x-axis is horizontal and the y-axis is vertical. The point where the x-axis and y-axis intersect is called the origin, and it is denoted by the coordinates (0, 0). The coordinates of a point on the coordinate grid are denoted by an ordered pair (x, y), where x is the x-coordinate and y is the y-coordinate.
Finding the Length of the Diagonal
The diagonal of a square is the line segment that connects two opposite vertices of the square. To find the length of the diagonal, we need to use the distance formula. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where d is the distance between the two points (x1, y1) and (x2, y2).
In this case, the coordinates of the two diagonally opposite vertices are (-2, 9) and (5, 2). We can use the distance formula to find the length of the diagonal:
d = √((5 - (-2))^2 + (2 - 9)^2) d = √((7)^2 + (-7)^2) d = √(49 + 49) d = √98 d = √(2 * 49) d = √2 * √49 d = 7√2
Finding the Midpoint of the Diagonal
The midpoint of a line segment is the point that divides the line segment into two equal parts. To find the midpoint of the diagonal, we need to use the midpoint formula. The midpoint formula is given by:
M = ((x1 + x2)/2, (y1 + y2)/2)
where M is the midpoint of the line segment with endpoints (x1, y1) and (x2, y2).
In this case, the coordinates of the two diagonally opposite vertices are (-2, 9) and (5, 2). We can use the midpoint formula to find the midpoint of the diagonal:
M = ((-2 + 5)/2, (9 + 2)/2) M = (3/2, 11/2) M = (1.5, 5.5)
Conclusion
In this article, we explored the concept of a square drawn on a coordinate grid, with two diagonally opposite vertices having coordinates (-2, 9) and (5, 2). We used the distance formula to find the length of the diagonal and the midpoint formula to find the midpoint of the diagonal. The length of the diagonal is 7√2 and the midpoint of the diagonal is (1.5, 5.5). We hope that this article has provided a clear understanding of the concept of a square drawn on a coordinate grid.
Further Reading
If you want to learn more about the concept of a square drawn on a coordinate grid, we recommend checking out the following resources:
References
Glossary
- Coordinate Grid: A system of two perpendicular lines that intersect at a point called the origin.
- Distance Formula: A formula used to find the distance between two points on a coordinate grid.
- Midpoint Formula: A formula used to find the midpoint of a line segment on a coordinate grid.
- Square: A four-sided shape with four right angles and four equal sides.
- Vertex: A point where two or more edges of a shape meet.