Placing Figures in the Coordinate Plane

Lesson 6-6

Review:

Angles of a KiteYou can construct a kite by joining two

different isosceles triangles with a common base and then by removing that common base.

Two isosceles triangles can form one kite.Two isosceles triangles can form one kite.

Angles of a Kite

Just as in an isosceles triangle, the angles between each pair of congruent sides are vertex anglesvertex angles. The other pair of angles are nonvertex anglesnonvertex angles.

Find the slope….

(a, b)

(3a, b+4)

Find the midpoint….

(a, b)

(3a, b+4)

Naming Coordinates

Rectangle KLMN is centered at the origin and the sides are parallel to the axes. Find the missing coordinates.

L(4, 3)

M(?, ?)

K(?, ?)

N(?, ?)

Answer:

K(-4, 3)

M(4, -3)

N(-4, -3)

Naming Coordinates

Rectangle KLMN is centered at the origin and the sides are parallel to the axes. Find the missing coordinates.

L(a, b)

M(?, ?)

K(?, ?)

N(?, ?)

Answer:

K(-a, b)

M(a, -b)

N(-a, -b)

Naming Coordinates Use the properties of a parallelogram to find the

missing coordinates. (Don’t use any new variables.

Q(?, ?)

P(s, 0)

K(b, c)

N(0, 0)

Answer:

Q(b + s, c)

Finding a Midpoint Find the coordinates of the midpoints

T, U, V, and W.

C(2c, 2d)

E(2e, 0)

A(2a, 2b)

O(0, 0)

W

V

U

T

Use midpoint formula:

2,

22121 yyxx

Answer:

T(a, b)

U(e, 0)

V(c + e, d)

W(a + c, b + d)

Finding a Slope

Find the slope of each side of OACE.

C(2c, 2d)

E(2e, 0)

A(2a, 2b)

O(0, 0)

W

V

U

T

Use slope formula:

12

12

xxyy

Answer:

slope of OA = b / a

slope of AC = d – b / c – a

slope of CE = c – e / d

slope of OE = 0

Midsegment of a trapezoid

The midsegment of a trapezoid is the segment that connects the midpoints of its legs. Theorem 6.17 is similar to the Midsegment Theorem for triangles.

midsegment

B C

DA

Theorem 6.17: Midsegment of a trapezoid

The midsegment of a trapezoid is parallel to each base and its length is one half the sums of the lengths of the bases.

MN║AD, MN║BC MN = ½ (AD + BC)

NM

A D

CB

Example

Find the value of x.

Mmmm cake.

5”

17”2nd layer?

14”

Assignment

Page 328 #’s 1-11 odd 20 , 23, 28-30, 31 Page 333 #’s 1 , 9