Integrated Math 1 / Unit 9: Coordinate Geometry and Constructions
9.4 Perimeter and Area on the Coordinate Plane
Notes
Use coordinates to find side lengths, then use geometry formulas.
- Horizontal or vertical sides: subtract coordinates. Slanted sides: use the distance formula.
- Rectangle: $P = 2(l + w)$, $A = lw$. Triangle: $\displaystyle A = \frac{1}{2}bh$.
- Perimeter is a length (units); area is in square units.
- Example: a triangle with vertices $(0, 0)$, $(8, 0)$, $(3, 6)$ has base 8 and height 6, so $\displaystyle A = \frac{1}{2}(8)(6) = 24$.
Practice
A rectangle has vertices $(1, 1)$, $(7, 1)$, $(7, 5)$ and $(1, 5)$. What is its perimeter?
Width is $7 - 1 = 6$ and height is $5 - 1 = 4$, so $P = 2(6 + 4) = 20$.
What is the area of the triangle with vertices $(0, 0)$, $(8, 0)$ and $(3, 6)$?
The base is 8 along the $x$-axis and the height is 6, so $\displaystyle A = \frac{1}{2}(8)(6) = 24$.
A triangle has vertices $A(0, 0)$, $B(3, 4)$ and $C(6, 0)$. What is its perimeter?
$\displaystyle AB = \sqrt{9 + 16} = 5$, $\displaystyle BC = \sqrt{9 + 16} = 5$ and $AC = 6$, so the perimeter is 16.
Ready for more? Take the Unit 9 test.