Math 1 · Unit 11 · Lesson 2 · part 3 of 4
Backward: find the missing endpoint
Now the backward question.
Backward: find the missing endpoint
Now the backward question. You know the midpoint and one endpoint. Where is the other endpoint? The midpoint M is (6, 2) and one endpoint A is (1, 3). Two ways, and you can pick.
The step way
The step from the endpoint to the midpoint is the same as the step from the midpoint to the other endpoint, because the halves are equal.
From A(1, 3) to M(6, 2): 5 right and 1 down.
Take that step once more from M: (6 + 5, 2 − 1) = (11, 1).
The equation way
The midpoint's x is the average of the two x's. Set it equal and solve the Unit 1 way.
1 + x2 = 6. Multiply both sides by 2: 1 + x = 12. Subtract 1: x = 11.
3 + y2 = 2. Multiply by 2: 3 + y = 4. Subtract 3: y = 1.
B = (11, 1).
Check: the midpoint of (1, 3) and (11, 1) is (1 + 112, 3 + 12) = (6, 2). It works.
One with negatives and decimals. Midpoint M(−1, −2), endpoint A(3.5, −7).
The step way
From A(3.5, −7) to M(−1, −2): the x goes from 3.5 to −1, a step of −4.5 (left 4.5). The y goes from −7 to −2, a step of +5 (up 5).
Once more from M: (−1 − 4.5, −2 + 5) = (−5.5, 3).
The equation way
3.5 + x2 = −1, so 3.5 + x = −2, so x = −5.5.
−7 + y2 = −2, so −7 + y = −4, so y = 3.
B = (−5.5, 3).