State the slopes of the parallel lines in the parallelogram below

Question

The base is the distance between points (-3, 3) and (3, 3), which is 6 units.

The height is the distance from point (0, 7) to the line y=3, which is 4 units

Area = (1/2) *base * height = (1/2) * 6 * 4
and the Area = 12 square units

Answer 1

To find the slopes of the parallel lines in the parallelogram you've described, we can start by analyzing the information provided:

1. The base of the parallelogram is defined by the line segment between the points (-3, 3) and (3, 3). Since both points have a y-coordinate of 3, this line is horizontal.

2. The slope of a horizontal line is 0.

Now, since we have a parallelogram, the sides opposite each other are parallel. Therefore, one pair of opposite sides (the base) has a slope of 0.

3. You also mentioned the height from point (0, 7) to the line \(y = 3\). The line that goes through point (0, 7) and is perpendicular to the base (the line \(y = 3\)) will have an undefined slope, indicating a vertical line.

In summary:

• The slopes of the parallel lines that form the base of the parallelogram are \(0\) (horizontal lines).
• The slopes of the lines forming the height (perpendicular to the base) are undefined (vertical lines).

Thus, in your parallelogram:

• Slopes of the parallel lines forming the base: 0
• Slopes of the parallel lines forming the height: undefined