Question

If the midpoint of points A and B is (3,-2) and endpoint A has coordinates (-3,0) what is the y-coordinate for the endpoint B

Answer 1

Greetings from Brasil...

We can solve this question quickly building the graph and verifying the given points - refer to attached

If the half of the line has the point Y = - 2, then in the whole line we will have the point Y = - 4. For X the same: Half of the line has 6 units (from -3 to 3 in module), so the whole line will have 12 units - refer to attached

After these observations we can conclude that

B(9; -4)

y-coordinate = - 4

Note that

d(A; M) = d(M; B) = 2√10

and

d(A; B) = 4√10

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There are other ways to resolve. We can use similarity of triangles OR the equation d(A; B) and d(M; B) which will result in an equation system with 2 variables