Answer:
To prove that ABCD is a parallelogram, we need to show that opposite sides are parallel. We can do this by calculating the slopes of each side and showing that they are equal.
The slope of a line passing through two points (x1,y1) and (x2,y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Using this formula, we can calculate the slopes of AB, BC, CD, and DA as follows:
Slope of AB:
slope_AB = (3 - 0) / (1 - 0) = 3
Slope of BC:
slope_BC = (4 - 3) / (0 - 1) = -1
Slope of CD:
slope_CD = (1 - 4) / (-1 - 0) = 3
Slope of DA:
slope_DA = (0 - 1) / (0 - (-1)) = 1
We can see that the slopes of AB and CD are equal, and the slopes of BC and DA are equal. Therefore, opposite sides of ABCD have equal slopes, which means they are parallel.
Hence, ABCD is a parallelogram.
Explanation: