Final answer:
To confirm that quadrilateral ABCD is a parallelogram, we calculate the slopes of opposite sides and show they are equal. The slopes are calculated using the coordinates of the vertices. If the slopes of opposite sides match, then ABCD is a parallelogram.
Step-by-step explanation:
To confirm that a quadrilateral ABCD is a parallelogram, one must demonstrate that opposite sides are parallel by showing they have the same slope. The slope of a line is calculated as the change in y divided by the change in x between any two points on the line, often referred to as 'rise over run'. For a four-sided figure described in the coordinates of a two-dimensional plane, we can calculate the slope of each side if the coordinates of the vertices are known.
For example, if side A has endpoints (x1, y1) and (x2, y2), then the slope of side A (mA) is calculated as (y2 - y1) / (x2 - x1). To confirm ABCD is a parallelogram, mA should equal mC (for opposite side C), and mB should equal mD (for the remaining opposite side D).
If a line graph is provided, like in Figure A1, with a slope (m) of 3 and a y-intercept (b) of 9, then the equation of that line can be described as y = 3x + 9. This information is useful for understanding how the slopes of lines work more generally but is not sufficient for confirming that a figure is a parallelogram without the specific coordinates of the quadrilateral's vertices.