4.1/4.2 distance, midpoint, slope and equations warm-up (in) learning objective: to find the...

4.1/4.2 Distance, Midpoint, Slope and Equations

Warm-up (IN)

Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify

polygons by their side lengths and to write equations of lines

Find the length of the 3rd side of each triangle:

1. a=4, b=7 2. a=6.3, c=12.4 3. b=43.1, c=157.8

Solve for b:

4. 5. 6. 3 2 3 b 1

2 22

b 23

5

b

8.1 or 10.765 151.8

-3 4.5 17

Notes

Distance Formula -

Given two points:

Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations

of lines

1 1 2 2, and ,A x y B x y

2 2

2 1 2 1d x x y y

Midpoint Formula -

1 2 1 2,2 2

x x y ymdpt

Slope Formula -

2 1

2 1

y ym

x x

Ex 1 – The vertices of Quad STAR are S(-1,4), T(3,5), A(4,1) and R(0,0).

a. Find the midpoints of the sides of the quad.

Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations

of lines

ST ,

2 2

1 3 4 5 1,4.5

TA

,2 2

3 4 5 1 3.5,3

AR

,2 2

4 0 1 0 2,0.5

Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations

of lines

RS ,

2 2

1 0 4 0 0.5,2

S(-1,4), T(3,5), A(4,1) and R(0,0)

b. Give the most specific name for STAR.

ST 2 2 3 1 5 4

ST 2 24 1 16 1 17

TA 2 2 4 3 1 5

TA 2 21 4 1 16 17

Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations

of lines

S(-1,4), T(3,5), A(4,1) and R(0,0)

AR 2 2 0 4 0 1

AR 2 24 1 16 1 17

SR 2 2 0 1 0 4

SR 2 21 4 1 16 17

Rhombus??

Or Square??

Find the lengths of the diagonals to see if the angles are right

SA 2 2 4 1 1 4

SA 2 25 3 25 9 34

S(-1,4), T(3,5), A(4,1) and R(0,0)

TR 2 2 0 3 0 5

TR 2 23 5 9 25 34

2

17 2

17 2

34 Right Square!!

Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations

of lines

Slope-intercept form of a line -

y=mx+b

slope y-int

Ex 2 – write the equation of the line…

a. With slope -3 and y-int -4 y=-3x-4

b. With slope 4 and contains (-2,8)

y=mx+b

8=

4(-2) +b

8=

-8 +b

16=

b

y=4x +16

Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations

of lines

c. contains (-2,8) and (4,2)

2 -8

4+2

=-6

6=-1

y=mx+b

2=

-1(4)+b

2=

-4 +b

6= b

y=- x +6

Horizontal lines

m=0y=#

vertical lines

m=undefined

x=#

Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations

of lines

HW – p. 169-170 #4,7,11,12

p. 176-177 #2,3,9-16

Out – None

Summary – Today, I learned…

POW!!