Answer:
b. A''(7, 5), B''(2, 5), C''(4, –1)
Step-by-step explanation:
Given vertices of ΔABC:
- A = (-1, 0)
- B = (4, 0)
- C = (2, 6)
Translation <u>mapping rule</u>:
(x, y) → (x – 6, y – 5)
Therefore:
- A' = (-1 - 6, 0 - 5) = (-7, -5)
- B' = (4 - 6, 0 - 5) = (-2, -5)
- C' = (2 - 6, 6 - 5) = (-4, 1)
Rotation of 180° clockwise rule:
(x, y) → (-x, -y)
Therefore:
- A'' = (-7, -5) = (7, 5)
- B'' = (-2, -5) = (2, 5)
- C'' = (-4, 1) = (4, -1)
Learn more about transformations here:
brainly.com/question/28354239
brainly.com/question/27743837
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
Answer is 512 cu.ft.
Volume of a cube is length x width x height
So 8 x 8 x 8 = 512
Answer:
1) 1/10
2) 1/2
3) 1/5
Step-by-step explanation:
1)
1 favorable outcome and 10 total outcomes.
2)
5 favorable outcomes and 10 total outcomes
3)
2 favorable outcomes and 10 total outcomes
