Step by step
The question
Question: find the other end B, when one end is A = (1, 3) and the midpoint is M = (−2, −1).
A = (1, 3) and M = (−2, −1)
1 Plot the points
Draw the grid.
Put the end A (1, 3) on the grid
and the midpoint M (−2, −1).
2 From A to M
From x = 1 to x = −2 we go left 3.
From y = 3 to y = −1 we go down 4.
3 Same moves again
M is in the middle.
So from M to the other end, the moves are the same: left 3, down 4.
Add the same moves to M: B = (−2 − 3, −1 − 4).
B = (−2 − 3, −1 − 4)
−2 minus 3 is −5.
−1 minus 4 is −5.
So B = (−5, −5).
B = (−5, −5)
Put B on the grid.
4 Check
Let's check: the midpoint of A and B.
The x's: 1 plus −5 is −4.
Half of it is −2.
x = 1 + (−5)2 = −42 = −2
The y's: 3 plus −5 is −2.
Half of it is −1.
We get M = (−2, −1) again.
Right!
y = 3 + (−5)2 = −22 = −1
Let's look back.
First: plot the points.
Then: from A to M.
Then: same moves again.
Last: check.
Answer
B = (−5, −5)