SAT Mc Graw Hill 2011

Working with Slopes

Every line has a slope, which is the distance you

move up or down as you move one unit to the

right along the line. Imagine walking between

any two points on the line. As you move, you go

a certain distance “up or down.” This distance

is called the rise. You also go a certain distance

“left or right.” This distance is called the run.

The slope is simply the rise divided by the run.

Slope =

rise

run

yy

xx

=

−

−

21

21

Plotting Points

Some SAT questions may ask you to work with points on
the x-yplane (also known as the coordinate plane or the
Cartesian plane, after the mathematician and philoso-
pher René Descartes). When plotting points, remember
these four basic facts to avoid the common mistakes:

• The coordinates of a point are always given
  alphabetically: the x-coordinate first, then
  the y-coordinate.


• The x-axis is always horizontal and the
  y-axis is always vertical.


• On the x-axis, the positive direction is to the
  right of the origin (where the xand yaxes
  meet, point (0,0)).


• On the y-axis, the positive direction is up
  from the origin (where the xand yaxes
  meet, point (0,0)).

You should be able to tell at a glance whether

a slope has a positive, negative,or zeroslope. If

the line goes up as it goes to the right, it has a

positive slope. If it goes down as it goes to the

right, it has a negative slope. If it’s horizontal,

it has a zero slope.

If two lines are parallel, they must have the

same slope.

y

x

(3, 5)

O 3 "right"

5 "up"

y

x

(x 2 ,y 2 )

(x 1 ,y 1 )

O

run = x 2 −x 1

rise = y 2 −y 1

y

x

O

positive slope

negative slope

0 slope

Finding Midpoints

The midpoint of a line segment is the point that

divides the segment into two equal parts.

Think of the midpoint as the average of the

two endpoints.

Midpoint =

xxyy 1212

22

⎛ ++

⎝⎜

⎞

⎠⎟

,

y

x

(x 2 ,y 2 )

(x 1 ,y 1 )

O

(

x 1 +x (^2) ,y 1 +y 2
2 2 )
378 McGRAW-HILL’S SAT
Lesson 4: Coordinate Geometry