Transcript 1.6 Midpoint and Distance in the Coordinate Plane

1.6
Midpoint and Distance in the
Coordinate Plane
Midpoint and Distance
• Coordinate Plane- a plane divided into four
regions by an x-axis and y-axis
• Midpoint Formula:
 x1  x2 y1  y2 
M 
,

2 
 2
Practice Problems:
1)Find the coordinates of the
midpoint of PQ with endpoints
P(–8, 3) and Q(–2, 7).
2)Find the coordinates of the
midpoint of EF with endpoints
E(–2, 3) and F(5, –3).
Practice Problems:
3)M is the midpoint of XY. X has
coordinates (2, 7) and M has
coordinates (6, 1). Find the
coordinates of Y.
4)S is the midpoint of RT. R has
coordinates (–6, –1), and S
has coordinates (–1, 1). Find
the coordinates of T.
Distance Formula
• Distance Formula:
d  ( x2  x1 )  ( y2  y1 )
2
2
Practice Problems:
5) Find FG and JK. Then determine whether
FG  JK.
F(1, 2)
G(5, 5)
J(-4, 0)
K(-1, -3)
Practice Problems
6) Find EF and GH. Then determine if EF 
GH.
E(-2, 1)
G(-1, -2)
F(-5, 5)
H(3, 1)
Right Triangles
leg
• Parts of a right triangle:
leg
Pythagorean Theorem
• For right triangles: the sum of the squares
of the length of the legs is equal to the
square of the length of the hypotenuse
a b  c
2
2
2
Practice Problems:
7) Use the Distance Formula and the
Pythagorean Theorem to find the
distance, to the nearest tenth, from D(3,
4) to E(–2, –5).