A square graphed on the coordinate plane has a diagonal with endpoints E (2,3) and F (0,-3) what are the coordinates of the endpoints of the other diagonal?
1 and -3
3
1
0654
64
To find the coordinates of the endpoints of the other diagonal, we need to find the midpoint of the given diagonal first.
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Using this formula, we can find the midpoint of the given diagonal by plugging in the given values:
Midpoint = ((2 + 0)/2, (3 + -3)/2)
= (2/2, 0/2)
= (1, 0)
Since a square has perpendicular diagonals that bisect each other, we can find the endpoints of the other diagonal by reflecting the midpoint across the origin (0,0).
Using the formula for reflection across the origin:
Reflection = (-x, -y)
Plugging in the midpoint coordinates (1,0):
Reflection = (-(1), -(0))
= (-1, 0)
Therefore, the coordinates of the endpoints of the other diagonal are (-1, 0) and (1, 0).
To find the coordinates of the endpoints of the other diagonal of a square, we need to understand the properties of squares and their diagonals.
In a square, the diagonals are perpendicular bisectors of each other. This means that the diagonals intersect at their midpoints and form right angles.
Given that we have the coordinates of one diagonal's endpoints, E (2,3) and F (0,-3), we can find the midpoint of the diagonal by averaging the x- and y-coordinates:
Midpoint (M) = ((x1 + x2) / 2 , (y1 + y2) / 2)
Substituting the given coordinates:
M = ((2 + 0) / 2 , (3 + (-3)) / 2)
= (1 , 0)
Since the diagonals of a square are perpendicular bisectors of each other, the midpoint (1,0) will also be the intersection point of the other diagonal.
Now, to find the coordinates of the endpoints of the other diagonal, we can use the distance formula from the midpoint to one of these points. Since a square has congruent sides, the distance from the midpoint to each of the endpoints will be the same.
Distance formula: √((x2 - x1)^2 + (y2 - y1)^2)
Let's consider the distance from the midpoint (1,0) to one of the known endpoints, E (2,3):
Distance (d) = √((2 - 1)^2 + (3 - 0)^2)
= √(1^2 + 3^2)
= √(1 + 9)
= √10
To find the coordinates of the other endpoint, we can move in two directions:
1. Move √10 units horizontally to the right from the midpoint (1,0):
Endpoint G: (1 + √10, 0) = (1 + √10, 0)
2. Move √10 units horizontally to the left from the midpoint (1,0):
Endpoint H: (1 - √10, 0) = (1 - √10, 0)
Therefore, the coordinates of the endpoints of the other diagonal are G (1 + √10, 0) and H (1 - √10, 0).