Chapter 7 Coordinate Geometry

Notes

Coordinate Geometry:

Study of points on graph Uses x-axis and y-axis

Cartesian Plane:

Horizontal line = x-axis Vertical line = y-axis Meeting point = origin (0,0)

Quadrants:

First quadrant → (+,+) Second quadrant → (-,+) Third quadrant → (-,-) Fourth quadrant → (+,-)

Distance Formula:

d= (x 2 ​

−x 1 ​

) 2 +(y 2 ​

−y 1 ​

) 2 ​

-10 -8 -6 -4 -2 2 4 6 8 10 -10 -5 5 10 A(6.0, 6.0) B(-6.0, -6.0) d = 16.97 Delta x = 12 Delta y = 12

Midpoint Formula:

( 2 x 1 ​

+x 2 ​

​

, 2 y 1 ​

+y 2 ​

​

) -10 -8 -6 -4 -2 2 4 6 8 10 -10 -5 5 10 A(-7.0, -3.0) B(5.0, 7.0) M = (-1.0, 2.0)

Section Formula:

( m+n mx 2 ​

+nx 1 ​

​

, m+n my 2 ​

+ny 1 ​

​

)

Important points:

On x-axis → y = 0 On y-axis → x = 0 Origin = (0,0)

Common mistakes:

Sign mistakes Wrong subtraction Confusing quadrants Forgetting square root