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