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2 answers:
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Given:
The figure.
To find:
The segment bisector of MN and value of MN.
Solution:
From the given figure it is clear that ray RP,i.e., is the segment bisector of MN because it divides segment MN in two equal parts.
Now,
Since, is the segment bisector of MN, therefore,
Therefore, the length of MN is .
So,
Let's translate this into mathematical form.
x - y = 9
x + 2y = 27
Elimination by Addition
Divide both sides of the second equation by 2
Add the two equations together
Multiply both sides by
Substitute
15 - y = 9
Subtract 15 from both sides
-y = -6
y = 6
Substitute
15 - 6 = 9
9 = 9 This checks.
15 + 2(6) = 27
Distribute
15 + 12 = 27
27 = 27 This also checks.
S = {(15,6)}
Let's translate this into mathematical form.
x - y = 9
x + 2y = 27
Elimination by Addition
Divide both sides of the second equation by 2
Add the two equations together
Multiply both sides by
Substitute
15 - y = 9
Subtract 15 from both sides
-y = -6
y = 6
Substitute
15 - 6 = 9
9 = 9 This checks.
15 + 2(6) = 27
Distribute
15 + 12 = 27
27 = 27 This also checks.
S = {(15,6)}