Slope
Equations of a Line
Midpoint & more
Triangle Time
perimeter and area
100
if you are given points (x1,y1) and (x2,y2) how can you find the rate of change (slope) between the two points?
m= (x2-x1)/(y2-y1)
100
What is the name of the form y-y1=m(x-x1)
point- slope form
100
What is the formula used to find the distance between two points?
distance formula:
sqrt((x2-x1)^2+(y2-y1)^2
100
The three medians of a triangle are concurrent at a point. What is this point called
The centroid
100
What is the lenth of side AB?
In what 2023 blockbuster movie would you hear the line, "I am Kenough"?
sqrt((2-1)^2 + (4-2)^2
sqrt(5)
200
What is the slope of the line parallel to y = 3x-1
3
200
Write an equation of a line with a slope of 5 and a y intercept of -1
y=5x-1
200
M(-5, 2) is the midpoint of AB. If point A is (-3, 6), what are the coordinates of point B?
(-7,-2)
200
In triangle ABC, the medians intersect at point G. If the full length of median CF is 24, what is the length of the shorter segment, FG?
8
200
What is the length of side BC
sqrt((3-2)^2 + (1-4)^2
sqrt(10)
300
What is the slope of a line perpendicular to the line
y= -2/3x-10
3/2
300
Which equation represents a line parallel to y=4x+6 and passes through the point (-3,2)
y-2=4(x+3)
300
A circle has its center at (3, -2) and passes through the point (7, 1). What is the length of its radius?
5
300
In a right triangle, the two legs have lengths of 3 inches and 5 inches. What is the length of the hypotenuse?
sqrt34
300
What is the area of triangle ABC
What three-letter sandwich, a breakfast staple, is famously ordered at a Long Island deli?
Box area = (2)(3)
T1= 1/2(1)(3)= 1.5
T2= 1/2(1)(2)=1
T3= 1/2(3)(1)=1.5
Area = 6 -(1.5+1+1.5)=2
400
What is the slope of a perpendicular line to the line 2x-y=7
-1/2
400
What two things must you find to write the equation of a perpendicular bisector?
The midpoint and the perpendicular slope
400
Find the coordinates of point F that divides the directed line segment DE from D(-4, -2) to E(1, 8) in a 2:3 ratio.
(-2,2)
400
In a right triangle, one leg has a length of 5 feet and the hypotenuse has a length of 13 feet. What is the length of the other leg?
12 feet
400
What is the area to triangle ABC
Box area = (5)(4)=20
T1= 1/2(1)(3)= 1.5
T2= 1/2(3)(2)=3
T3= 1/2(5)(2)=5
Area = 20 -(1.5+3+5)=11.5
500
A line passes through (1,4) and (3,y). If the slope is -2, what is the value of y?
y=0
500
What is the equation of the perpendicular bisector of NY, which has endpoints N(-11,5) and Y(5,-7)
y+1=4/3(x+3)
500
A circle has its center at (3, -2) and passes through the point (7, 1). What is the length of its diameter?
10
500
Two sides of a triangle have lengths of 2 and 8. The length of the third side must be greater than what number and less than what number?
hint: triangle inequlity theorem
greater than 6 and less than 10
500
Is this triangle a right triangle?
No, There are no two lines where the slopes are negative reciprocals.
Slope AB= (5-1)/(3-1)=4/2=2
Slope BC=(5-3)/(3-6)=2/-3
Slope AC=(3-1)/(6-1)=2/5