SOLUTION: Show that the points R (-1 , 2), K (5 , 2) and O (2 , 5) are the vertices of an isosceles triangle. Find the area of triangle RKO. :) =)

Algebra ->  Algebra  -> Coordinate-system -> SOLUTION: Show that the points R (-1 , 2), K (5 , 2) and O (2 , 5) are the vertices of an isosceles triangle. Find the area of triangle RKO. :) =)       Log On

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Question 403267: Show that the points R (-1 , 2), K (5 , 2) and O (2 , 5) are the vertices of an isosceles triangle. Find the area of triangle RKO.
:) =)
Answer by Alan3354(30927) About Me  (Show Source):
You can put this solution on YOUR website!
Show that the points R (-1,2), K (5,2) and O (2,5) are the vertices of an isosceles triangle.
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Find the lengths of RO and KO
s%5E2+=+diffy%5E2+%2B+diffx%5E2
For RO:
s%5E2+=+3%5E2+%2B+3%5E2+=+18
For KO:
s%5E2+=+3%5E2+%2B+3%5E2+=+18
They're the same length --> isoceles.
The length of KR = 6 --> not equilateral.
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Find the area of triangle RKO.
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Write the points in columns, repeating the 1st point
R K O R
-1 5 2 -1
+2 2 5 +2
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Add the diagonal products from upper left:
(-1*2) + 5*5 + 2*2 = 27
Add the diagonal products from lower left:
2*5 + 2*2 + 5*(-1) = 9
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The area = 1/2 the difference
Area = (1/2)*(27-9) = 9 sq units