Answers:
- a) -3
- b) 7/3
- c) -1/2
- d) 1/11
- e) undefined
- f) 0
- d) 2/3
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Step-by-step explanation:
If the original slope is a/b, then the perpendicular slope is -b/a
We flip the fraction and we flip the sign from positive to negative, or vice versa.
As an example, the slope 1/3 flips its fraction to 3/1 or just 3. Then we flip the sign to -3. So if the original slope is 1/3, then its perpendicular counterpart is -3.
Notice how the two slopes multiply to -1
(1/3)*(-3) = -1
This applies to any pair of perpendicular lines such that neither line is horizontal and neither line is vertical either.
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If the original slope is some whole number, then rewrite it as a fraction over 1
Example: 2 becomes 2/1
That way we can flip the fraction and the sign
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If we had an original slope of 0, then it's the same as 0/1
Flipping the fraction leads to 1/0, but that's undefined. We cannot divide by zero. So that explains the answer to part e).
Going in reverse of this process, any line with undefined slope will be perpendicular to lines of slope 0.
horizontal lines have slope of 0
vertical lines have undefined slopes
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For part g), you'll need to convert from a mixed number to an improper fraction
Use this formula
a & b/c = (a*c + b)/c
So this means,
1 & 1/2 = (1*2 + 1)/2 = 3/2
which leads to
-1 & 1/2 = -3/2
Then applying the rule "flip the fraction flip the sign" gets us from -3/2 to 2/3.