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 (divide 24/2=12)

Answer 1

To find the slopes of the parallel lines in the parallelogram, we first need to establish the coordinates and the way the lines are defined.

1. The base of the parallelogram is defined by the points (-3, 3) and (3, 3). The slope of this base line can be determined as follows:

   • Since both points have the same y-coordinate (y = 3), the line is horizontal.
   • The slope of a horizontal line is \(0\).

2. The height is mentioned as the distance from the point (0, 7) to the line \(y = 3\). To find the slope of the other set of parallel lines, we need to look at the line that would connect the point (0, 7) vertically down to the base.

   • Since this line is vertical (from (0, 7) to (0, 3)), its slope is undefined (or considered to be infinite).

In a parallelogram, opposite sides are parallel and thus have the same slope. Given this information:

• The parallel lines at the base of the parallelogram have a slope of \(0\).
• The height lines (the other pair of parallel sides) would have an undefined slope.

In summary:

• Slope of the first set of parallel lines (base lines): \(0\)
• Slope of the second set of parallel lines (height lines): undefined

These slopes dictate that one pair of opposite sides is horizontal while the other pair is vertical.