Question 80689: I've been trying to figure a few of these equations all day, but I can't seem to understand the how to find the slopes and graphs and I'm getting more homework than I can keep up with. Also is there a more simple explanation of how to find whether points are parallel or perpendicular? Is there a way I can get some one on one tutoring, either from here or another program?
-find the slope of any line perpendicular to the line through points (0,5) and
(-3,-4)
-Floor plans for a building have the four corners of a room 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 perpendicular to the sides through the points (2,3) and (-3,18).
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!First lets find the slope through the points (0,5) and (-3,-4)
note: check out this solver to get more help with finding the slope
| Solved by pluggable solver: Finding the slope |
To find the slope going from (0,5) to (-3,-4) we are going to calculate the change in y over the change in x, or the rise over the run. The change is the difference between the two coordinates. So if the y-coordinate of a point goes from 5 to -4, the change in these numbers is -9 (since  ). If the x-coordinate changes from 0 to -3, then the change is -3 (since  ). So to calculate the slope we use this formula:
Slope:
 where m is the slope
So now we let  , , , Now plug these numbers into the slope formula:
So after simplification the slope is  |
Since the perpendicular slope is the negative inverse of the original slope, we can say the perpendicular slope is
 where  is the perpendicular slope
So plug in m=3 to get
So the perpendicular slope is
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"Floor plans problem"
First lets find the slope through (2,3) and (11,6)
| Solved by pluggable solver: Finding the slope |
To find the slope going from (2,3) to (11,6) we are going to calculate the change in y over the change in x, or the rise over the run. The change is the difference between the two coordinates. So if the y-coordinate of a point goes from 3 to 6, the change in these numbers is 3 (since  ). If the x-coordinate changes from 2 to 11, then the change is 9 (since  ). So to calculate the slope we use this formula:
Slope:
where m is the slope
So now we let  , , , Now plug these numbers into the slope formula:
So after simplification the slope is  |
Now lets find the slope through (2,3) and (-3,18)
| Solved by pluggable solver: Finding the slope |
To find the slope going from (2,3) to (-3,18) we are going to calculate the change in y over the change in x, or the rise over the run. The change is the difference between the two coordinates. So if the y-coordinate of a point goes from 3 to 18, the change in these numbers is 15 (since  ). If the x-coordinate changes from 2 to -3, then the change is -5 (since  ). So to calculate the slope we use this formula:
Slope:
where m is the slope
So now we let  ,,,Now plug these numbers into the slope formula:
So after simplification the slope is  |
Notice that the side that contains the points (2,3) and (11,6) has a slope of . Also notice that the side containing (2,3) and (-3,18) has a slope of . So to see if they are perpendicular we simply invert and negate either slope. For instance, lets invert and negate the first slope :
So the perpendicular slope is -3. This shows that -3 and 1/3 are perpendicular slopes which means the two sides are perpendicular.
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