A(–4, 3), B(3, 7), C(0, –1) and D(–7, –5) are the vertices of a parallelogram on the Cartesian plane.
Determine the coordinates of the point where the diagonals of ABCD intersect.
find the equations (point-slope) of the diagonals and set them equal
actually, slope-intercept is better
I'd just find the midpoint of AC or BD, since the diagonals bisect each other.
good solution, Steve
To find the coordinates of the point where the diagonals of ABCD intersect, you can use the formula for the midpoint of a line segment.
The diagonals of a parallelogram bisect each other, which means that the point of intersection is the midpoint of both diagonals.
Let's consider the diagonals of ABCD: AC and BD.
The coordinates of point A are (-4, 3), and the coordinates of point C are (0, -1).
Using the midpoint formula, the x-coordinate of the point where AC intersects can be found by taking the average of the x-coordinates of A and C:
x-coordinate: (x1 + x2) / 2 = (-4 + 0) / 2 = -2.
Similarly, the y-coordinate of the point where AC intersects can be found by taking the average of the y-coordinates of A and C:
y-coordinate: (y1 + y2) / 2 = (3 + (-1)) / 2 = 1/2.
So, the coordinates of the point where AC intersects are (-2, 1/2).
Now let's find the coordinates of the point where BD intersects.
The coordinates of point B are (3, 7), and the coordinates of point D are (-7, -5).
Using the midpoint formula, the x-coordinate of the point where BD intersects can be found by taking the average of the x-coordinates of B and D:
x-coordinate: (x1 + x2) / 2 = (3 + (-7)) / 2 = -2.
Similarly, the y-coordinate of the point where BD intersects can be found by taking the average of the y-coordinates of B and D:
y-coordinate: (y1 + y2) / 2 = (7 + (-5)) / 2 = 1.
So, the coordinates of the point where BD intersects are (-2, 1).
Therefore, the coordinates of the point where the diagonals of ABCD intersect are (-2, 1).