Geometry 8.6.3 - Equations of Parallel and Perpendicular Lines and Proofs
1 answer:
Option B:
<u>Solution:</u>
<u>Slope of the perpendicular lines:</u>
If two lines are perpendicular then their slopes are negative reciprocals of each other.
<u>Slope of the parallel lines:</u>
If two lines are parallel then they have the same slope.
i.e their slopes are equal.
Given line m and p are parallel.
Slope of the line m =
Using slope of the parallel lines definition,
Slope of the line p = slope of the line m
Slope of the line p =
Option B is the correct aswer.
Hence the slope of the of line p is .
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Step-by-step explanation:
This is a Combination (as in permutation vs combination) question the symbol (n r) refers to "n choose r". This is sometimes written as nCr
i.e the question is asking you to find how many combinations each will yield when you chose r items from n item without repetition and order does not matter.
I will only do the first question for you and you can just follow the same steps to solve the rest of the questions.
Recall that
Consider question a) we are given (5 1) or ₅C₁
we can see that n = 5 and r = 1
If we substitute this into the formula:
₅C₁ = (5!) / [ (1!)(5- 1)!]
= (5!) / [ (5- 1)!]
= (5!) / (4!)
= (5·4·3·2·1) / (4·3·2·1)
= 5
hence ₅C₁ = 5