1. M is the midpoint of LN and O is the midpoint of NP. This makes the triangle MNO equal to half of LNP. Then you can get this equation
MO= (1/2) LP
If you insert MO = 2x +6 and LP = 8x – 20 the calculation would be:
2x+6= (1/2)( 8x-20)
2x+6= 4x-10
2x-4x= -10 - 6
-2x= -16
x=8
2. Centroid is the point that intersects with three median lines of the triangle. The centroid should divide the median lines into 1:2 ratio. In AC lines, A located in the base so A.F:FC would be 1:2
Then, the answer would be:
A.F= 1/(1+2) * AC
A.F= 1/3 * 12= 4
FC= 2/(1+2) * AC
FC= 2/3 * 12= 8
3. Since
∠BAD=∠DAC
∠ABD=∠ACD
AD=AD
The triangle ABD and ACD are similar. You can get this equation
BD=DC
x+8= 3x+12
x-3x= 12-8
-2x=4
x=-2
DC=3x+12= 3(-2) +12= 6
4. Orthocenter made by intersection of triangle altitude
A
BC lines slope would be (-4)-(-1)/1-4= -3/-3= 1. The altitude line slope would be -1, the function would be:
y=-x +a
0= 1+a
a=-1
y=-x-1
B
AC lines slope would be (-4)-(-1)/1-0= -3. The altitude line slope would be 1/3, the function would be:
y=1/3x+a
-1=1/3(4)+a
a=-7/3
y=1/3x - 7/3
C
BC lines slope would be (-1)-(-1)/4 = 0/4.
The line would be
0=x+a
a=-1
0=x-1
x=1
y=-x-1 = 1/3x-7/3
-x-(1/3x)=-7/3 +1
-4/3x= -4/3
x=1
y=-x-1
y=-1-1= -2
The orthocenter would be (1,-2)
5.
a. Circumcenter: the intersection of perpendicular bisector lines<span>
b. Incenter: the intersection of bisector lines
c. Centroid: </span>the intersection of median lines<span>
d. Orthocenter: </span>the intersection of altitude lines
1. -3x + -6
2. -3x + 9
3. 2x - 6
4. -2x + 6
here u go
The slope of this line is -1/6.
2 Point: (6,2) (-6,6)
x₁ y₁ x₂ y₂
Remember:
rise change in y y₂ - y₁ 6 - 2 4
---------- = ------------------- = ------------- = ----------- = ----------
run change in x x₂ - x₁ -6 - 6 -12
Simplify 4/-12
4 ÷ 4 1
------- = ------------- = -1/3
-12 ÷ 4 -3
The slope of the line is -1/3.
M² - 12m + 20
m² ⇒ m * m
20 ⇒ - 10 * -2
(m - 10)(m - 2)
m(m - 2) - 10(m-2)
m² - 2m - 10m + 20
m² - 12m + 20
m - 10 = 0
m = 10
m - 2 = 0
m = 2
X=5 because you add 2 to both side and get 3x=15, and then you divide both sides by 3 to get x alone, and get 15/3 which equals 5
