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What are the values of a and b if 6 3 is the midpoint of the line joining 2a comma 2a-b to a-2b comma 4a plus 3b?
6 is the average of 2a and a - 2b so 12 = 2a + a - 2b = 3a - 2b
3 is the average of 2a - b and 4a + 3b so 6 = 2a - b + 4a + 3b = 6a + 2b
Adding the two equations gives: 18 = 9a so that a = 2
Substituting for a in the first gives 12 = 6 - 2b so that b = -3
6 is the average of 2a and a - 2b so 12 = 2a + a - 2b = 3a - 2b
3 is the average of 2a - b and 4a + 3b so 6 = 2a - b + 4a + 3b = 6a + 2b
Adding the two equations gives: 18 = 9a so that a = 2
Substituting for a in the first gives 12 = 6 - 2b so that b = -3
6 is the average of 2a and a - 2b so 12 = 2a + a - 2b = 3a - 2b
3 is the average of 2a - b and 4a + 3b so 6 = 2a - b + 4a + 3b = 6a + 2b
Adding the two equations gives: 18 = 9a so that a = 2
Substituting for a in the first gives 12 = 6 - 2b so that b = -3
6 is the average of 2a and a - 2b so 12 = 2a + a - 2b = 3a - 2b
3 is the average of 2a - b and 4a + 3b so 6 = 2a - b + 4a + 3b = 6a + 2b
Adding the two equations gives: 18 = 9a so that a = 2
Substituting for a in the first gives 12 = 6 - 2b so that b = -3
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