Question

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.

Answer 1

Answer:

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 2

Answer:

it’s C’(4,-2)

Step-by-step explanation: