SAT Mc Graw Hill 2011

The Distance Formula:

d^2 =(x 2 −x 1 )^2 +(y 2 −y 1 )^2

so

y

x

(x 2 ,y 2 )

(x 1 ,y 1 )

O

x 2 – x 1

y 2 – y 1

d

dxx yy=−() 21 +−()

2

21

2

30 °-60°-90°triangles These triangles can

be thought of as equilateral triangles cut in half.

Thisshows why the angles and sides are re-

lated the way they are. Notice that the sides

satisfy the Pythagorean theorem.

The Distance Formula

Say you want to find the distance between two points
(x 1 , y 1 ) and (x 2 , y 2 ). Look carefully at this diagram
and notice that you can find it with the Pythagorean
theorem. Just think of the distance between the
points as the hypotenuse of a right triangle, and the
Pythagorean theorem becomes—lo and behold—
the distance formula!

60 °

2 x 30 °

x

x 3

372 McGRAW-HILL’S SAT