Triangle abc is shown on the coordinate grid.
part a:
translate δ a b c 6 units horizontally. how are the values in the ordered pairs affected by the translation?
part b:
translate
δ
a
b
c
3 units vertically. how are the values in the ordered pairs affected by the translation?
part c:
how could you determine the coordinates of the vertices of a translated image without using a graph?
the figure shows a triangle upperword abc on the coordinate grid. the values on the x-axis range from negative 8 to 8 in increments of 2 and the values on the y-axis range from negative 8 to 8 in increments of 2. the coordinates of the vertices upper a, upper b, and upper c are labeled as (negative 4, 1), (negative 1, 1), and (negative 1, 4) respectively.

Part A: The x-coordinates of points A, B , C are add or subtract by 6

Part B: The y-coordinates of points A, B , C are add or subtract by 3

Part C: A' = (-4 ± 6 , 1 ± 3) , B' = (-1 ± 6 , 1 ± 3) , C' = (-1 ± 6 , 4 ± 3)

Step-by-step explanation:

* Lets explain the answer

- If a point (x , y) is translated horizontally h units to the right, then

 its image is (x + h , y)

- If a point (x , y) is translated horizontally h units to the left, then

 its image is (x - h , y)

- If a point (x , y) is translated vertically k units up, then its image

 is (x , y + k)

- If a point (x , y) is translated vertically k units down, then its image

 is (x , y - k)

* Lets solve the problem

- Triangle ABC has vertices A = (-4 , 1) , B = (-1 , 1) , C = (-1 , 4)

# Part A:

∵ Δ ABC translated 6 units horizontally

∴ The x-coordinates of points A, B , C are add or subtract by 6

- If the triangle translated to the right then each x-coordinate of

 points A, B , C added by 6

- If the triangle translated to the left then each x-coordinate of

 points A, B , C subtracted by 6

# Part B:

∵ Δ ABC translated 3 units vertically

∴ The y-coordinates of points A, B , C are add or subtract by 3

- If the triangle translated up then each y-coordinate of points

  A, B , C added by 3

- If the triangle translated down then each y-coordinate of points

 A, B , C subtracted by 3

# Part C

∵ The vertices of Δ ABC are A = (-4 , 1) , B = (-1 , 1) , C = (-1 , 4)

- The triangle translated 6 units horizontally and 3 units vertically

∴ The images of its vertices are:

  A' = (-4 ± 6 , 1 ± 3) , B' = (-1 ± 6 , 1 ± 3) , C' = (-1 ± 6 , 4 ± 3)

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,