Step by step
The question
Question: find the midpoint of (−3, 4) and (5, 10).
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Plot the points
Draw the grid.
Put both points on the grid: (−3, 4)
and (5, 10).
Join them with a straight line.
We want its middle.
2 Middle of the x's
The midpoint is halfway across.
Halfway between two numbers: add them, then divide by 2.
−3 plus 5 is 2.
2 divided by 2 is 1.
So x = 1.
Is 1 really in the middle?
From −3, a jump of 4 gives 1.
From 1, 4 more gives 5.
The same jump from each end.
So adding and halving finds the middle.
3 Middle of the y's
Now the y's: the same.
Add them, then divide by 2.
4 plus 10 is 14.
14 divided by 2 is 7.
So y = 7.
4 The midpoint
So the midpoint is M = (1, 7).
Put M on the grid.
It sits on the line, right in the middle.
5 Check
Let's check on the grid.
From (−3, 4) to M:
we go right 4, up 3.
From M to the other point:
we go right 4, up 3.
The same moves.
So M is exactly in the middle!
6 Pick the choice
Our answer is M = (1, 7).
That is choice A.
7 Why not the others
B is (2, 14).
Wrong: added, but forgot to halve.
C is (4, 3).
Wrong: took away instead of adding.
D is (8, 6).
Wrong: took away and forgot to halve.
Let's look back.
First: plot the points.
Then: middle of the x's.
Then: middle of the y's.
Then: the midpoint.
Then: check.
Then: pick the choice.
Last: why not the others.