this problem seems with too many numbers that i don't know where to start. or even how.I have to answer the problem on top not the one that says number 27.

The problem:
Geometry. For the floor plans given in exercise 27, determine whether the side through the points (2,3) and (11,6) is perpendicular to the side through the points (2,3) and (-3,18).
# 27 states the following: Geometry. Floor plans for a building have the four corners of a room located at the points (2,3), (11,6), (-3,18), and (8,21). Determine whether the side through the points (2,3) and (11,6) is parallel to the side through the points (-3,18) and (8,21).

Compute the slopes of the four lines they have mentioned. I know you can do that from other work you have posted here.

They are asking of two of the line pairs are perpendicular, and if another pair are parallel.

If the slopes of the two lines are the same, they are parallel.

If the product of the slopes of two lines is -1, the lines are perpendicular. (Trust me; there is a theorem that proves that)

I will try then i will repost for you to check for me please....

Yes, you are on the right track! To determine whether the side through the points (2,3) and (11,6) is perpendicular to the side through the points (2,3) and (-3,18), you can follow these steps:

1. Calculate the slope of the first line:
- The formula to calculate the slope between two points (x1, y1) and (x2, y2) is (y2 - y1) / (x2 - x1).
- In this case, the two points are (2,3) and (11,6).
- Substitute the values into the formula: slope = (6 - 3) / (11 - 2).

2. Calculate the slope of the second line:
- The two points for the second line are (2,3) and (-3,18).
- Substitute the values into the formula: slope = (18 - 3) / (-3 - 2).

3. Compare the slopes:
- If the slopes are the same, then the lines are parallel.
- If the product of the slopes is -1, then the lines are perpendicular.

So, in this case, you need to calculate the slopes of the two lines and then analyze the results to determine whether they are parallel or perpendicular. Once you have calculated the slopes, you can post them here for me to check if they are correct!