# Rectangular Coordinate System: The Cartesian Plane 1.1,

```Rectangular
Coordinate System:
The Cartesian Plane
1.1, and Review
Review: Equations
9x − 10 = 5x + 2(2x − 5)
17+y
y
√
+
32+y
y
= 100
5−x−3=2
|2x + 1| = 7
Vocab.
!   coordinate pair – (x, y)
!   x-coordinate
!   y-coordinate
!   x-axis and y-axis
!   the origin
Formulas
!   Midpoint Formula
!   Given 2 points (x1, x2) and (y1, y2) the midpoint, M, is:
2 y1 +y2
M ( x1 +x
, 2 )
2
!   Distance Formula
!   Given 2 points (x1, x2) and (y1, y2) the distance between
them, d, is:
d=
�
(x2 − x1 )2 + (y2 − y1 )2
!   Pythagorean Theorem (only works for right triangles)
where h is the length of the hypotenuse and a &amp; b are the length of the legs
a 2 + b 2 = h2
Examples:
!   Ex. 1: Find coordinates of a point 10
units to the left of y-axis and 3 units
above the x-axis.
!   Ex. 2: If –x &gt; 0 and y &lt; 0, what
Examples cont.
!   Ex. 3: : Find the distance between
(-3, -2) and (4, 1).
!   Ex. 4: Find the midpoint of the line
segment between (5, 2) and (-3, -1).
Examples cont.
!   Ex. 5: An airplane flies from Naples,
Italy in a straight line to Rome, Italy,
which is 120 km north and 150 km
west of Naples. How far does the
plane fly?
Examples cont.
!   Ex. 6: A room is 1&frac12; times as long as
it is wide, and its perimeter is 25
meters. Find the dimensions of the
room.
Review: Inequalities
1 &lt; 2x + 3 ≤ 9
−4(x + 1) &lt; 2x + 3
|x − 20| ≤ 6
|9 − 2x| − 2 &gt; −1
Identify &amp; Correct the error:
Ex. 1:
5 &divide; 50 = 50 &divide; 5
Ex. 2:
8 − (x + 2) = (8 + 2) + x = x +10
Identify &amp; Correct the error:
Ex. 3:
2
2
(a + b) = a + b
2
Ex. 4:
€
1
(1/ x) + 2 =
x +2
Identify &amp; Correct the error:
Ex. 5:
3
2x = (2x)
3
Ex. 6:
€
−x + k = − x − k
Identify &amp; Correct the error:
Ex. 7:
m
m m
= +
x+n x n
Ex. 8:
€
a + bx
= 1+ bx
a
```