THE DISTANCE FORMULA
Distance in the Coordinate Plane
Standard:
8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Objectives
Essential Question for Topic
Deductive reasoning is a process of reasoning logically from given facts to a conclusion. If you do not have measuring tools, how can you deduce what the side lengths are of a right triangle? How can you deduce that a triangle is right?
DISTANCE FORMULA
THE DISTANCE FORMULA |
Given the two points (x1, y1) and (x2, y2), the distance between these points is given by the formula: √ (X1 –X2)2 + (Y1-Y2)2 |
Recall: You pick which point is first, then second.
The diagram below shows the relationship between the Distance Formula and the coordinates of two endpoints of a line segment.
√ (X1 –X2)2 + (Y1-Y2)2
A
L
E
R
T
!
EXAMPLE: Finding the length of a segment, given its endpoints
√ (X1 –X2)2 + (Y1-Y2)2
Let’s Practice:
What is the distance between the points (5, 6) and (– 12, 40) ?
Let’s Practice:
Find the lengths of the segments. Tell whether any of the segments have the same length. Use the Distance Formula.
A (-1,1)
C (3,2)
AC = ___
A (-1,1)
D (2,-1)
AD = __
A (-1,1)
B (4,3)
AB = ___
AB = √13; AC = √17; AD = √13
Now, it’s your turn…..
What is the distance between (–2, 7) and (4, 6)?
What is your answer? _________
What is the distance between (–1, 1) and (4, 3)?
What is your answer? _________
ALGEBRA CHALLENGE: If the distance from (x, 3) to
(4, 7) is √41 , what is the value of x?
What is your answer? _________
Check your answers HERE.
6.08
√13
9
Final Checks for Understanding
C (0,0)
D (5,2)
2. Use the Distance Formula to determine if JK = KL.
J(3,-5); K(-1,2) ; L (-5,-5)
_________________________________
J (3,-5)
K (1,2)
JK=
K (1,2)
L (-5,-5)
KL=