Step by step
The question
Question: find the area of the rectangle with corners (1, −4), (4, −4), (4, 2), (1, 2).
rectangle: (1, −4), (4, −4), (4, 2), (1, 2)
1 Plot the points
We put the corners on the grid.
Corner A is (1, −4).
And so on.
We join them in order.
2 Find the side lengths
A B: the same y, so it goes across.
Its length is the bigger x minus the smaller: 4 minus 1 is 3.
= AB: 4 − 1 = 3
B C: the same x, so it goes up and down.
Its length is the bigger y minus the smaller: 2 minus −4 is 6.
= BC: 2 − (−4) = 6
Careful!
−4 is on the other side of 0.
Minus a negative is plus: 2 plus 4.
Careful: not 2 − 4 = -2 ✗
3 Area
The area of a rectangle is length times width.
= area = length × width
3 times 6 is 18 square units.
= area = 3 × 6 = 18 square units
4 Check
Let's check: count the squares inside.
6 rows of 3 squares: 18.
So the answer is right!
6 rows of 3 squares = 18 squares
Let's look back.
First: plot the points.
Then: find the side lengths.
Then: area.
Last: check.
Answer
= area = 3 × 6 = 18 square units