1. 4.1/4.2 Distance, Midpoint, Slope and Equations
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
Warm-up (IN)
Find the length of the 3rd side of each triangle:
1. a=4, b= a=6.3, c= b=43.1, c=157.8
Solve for b:
8.1 or
10.7
151.8 -3
4.5 17

2. Notes Given two points: Distance Formula - Midpoint Formula -
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
Notes
Given two points:
Distance Formula -
Midpoint Formula -
Slope Formula -

3. 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
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.

4. b. Give the most specific name for STAR.
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)
b. Give the most specific name for STAR.

5. S(-1,4), T(3,5), A(4,1) and R(0,0) Rhombus?? Or 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
S(-1,4), T(3,5), A(4,1) and R(0,0)
Rhombus??
Or Square??

6. Find the lengths of the diagonals to see if the angles are right
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 lengths of the diagonals to see if the angles are right
S(-1,4), T(3,5), A(4,1) and R(0,0)
Right
Square!!

7. Slope-intercept form of a line -
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= -3 x -4
b. With slope 4 and contains (-2,8)
y=mx+b
(-2) +b x
+16 8= 4 y= 4 8= -8 +b
16= b

8. c. contains (-2,8) and (4,2) y=mx+b 2 -8 -1 (4) +b y= - x +6 -6 2= = =
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)
y=mx+b 2 -8 -1
(4) +b y= - x +6 -6 2= = = -1 4 +2 6 2= -4 +b 6= b
Horizontal lines
vertical lines
m=0
m=undefined
y=#
x=#

9. Out – None
Summary – Today, I learned…
HW – p #4,7,11,12
p #2,3,9-16