Use the Pythagorean Theorem, c²=a2+ b², to derive the distance formula.
96
B(4,7)
(xx)
Given: Points A, B, C.
210
A(1,3) C(4,3)
(xx) (xx)
Prove: The distance, d, between points A and B is v(x-x)+(-*.
(AC)=(AB)+(BC)
(BC)=(AB)²+(AC)
(AC)=(x-x)+(-) (BC)=(x-x₁)²+(15-4)³
AC = √√x-x)+(-) BC=√√√(x-x₁)²+(1-x)³
d = √(x-x)+(1-x)³d = √(x-x)²+(x-4)²
W. X.
(AB) (AC)+(BC)
(AB)'= (Ad)²+(BC)
(AB)=(x-x)+(-) (AB)=(x-x)²+(x-x₁)
AB =√√x-x)+(-) AB =√(x-x)²+(1-x)²
Y. Z.

A. Y
B. X
C. W
D. Z