Step by step
The question
Question: find the area of the triangle with corners (−4, 1), (1, 1), (−2, −3).
1 Plot the points
We put the corners on the grid.
Corner A is (−4, 1).
And so on.
We join them in order.
2 Find the base and height
base A B: the same y, so it goes across.
Its length is the bigger x minus the smaller: 1 minus −4 is 5.
Careful!
−4 is on the other side of 0.
Minus a negative is plus: 1 plus 4.
The height goes straight up from C to the base line.
It goes from y = −3 to y = 1: 4 units.
3 Area
The area of a triangle is a half times base times height.
Half of 5 times 4 is 10 square units.
4 Check
Let's check: the rectangle around the base and the height is 5 by 4: 20 squares.
The triangle takes half of it: 10.
So the answer is right!
Let's look back.
First: plot the points.
Then: find the base and height.
Then: area.
Last: check.