This problem tests your general understanding of coordinate geometry. The following information is needed to solve these problems:
In these problems, you should start by finding the coordinates of all four corners of the given rectangle (or as many
as you will need). Then you can proceed to find any midpoints that you would need to solve the problem.
You are given rectangle ABCD with diagonals AC and BD. The diagonals intersect at point E.
The coordinates of D are (0,3).
The coordinates of B are (6,7).
Find the coordinates of the midpoint of AB.
Since point A
is on the same vertical line as point D
it must have the same (x
. Since it is on the same horizontal line as point B, it must have the same
-coordinate as B. Therefore, the coordinates of A
are (0,7). We could similarly work out the coordinates of C
are (6,3)), though they are not needed in this problem.
We are asked to find the midpoint of AB
. We do this by using the midpoint formula.
Starting with the coordinates of A
A = (0,7), so x1 = 0 and y1 = 7
B = (6,7), so x2 = 6 and y2 = 7
So, xm = (0 + 6) / 2 = 3 and ym = (7 + 7) / 2 = 14
So the coordinates of the midpoint of AB are (3, 7).