Questions: Using triangle ABC, translate 6 to the right and down 10 then translate 8 left and 2 up A(1,5) B(6,2) C(8,11) a. Translate 6 to the right and down 10 A'(,) B'(,) C'(, b. Translate 8 left and 2 up A''(,) B''(,) C''(,

Using triangle ABC, translate 6 to the right and down 10 then translate 8 left and 2 up
A(1,5) B(6,2) C(8,11)
a. Translate 6 to the right and down 10 A'(,) B'(,) C'(,
b. Translate 8 left and 2 up A''(,) B''(,) C''(,

Transcript text: Using $\triangle A B C$, translate 6 to the right and down 10 then translate 8 left and 2 up $A(1,5) B(6,2) C(8,11)$ a. Translate 6 to the right and down 10 $A^{\prime}(,) B^{\prime}(,) C^{\prime}($, b. Translate 8 left and 2 up $A^{\prime \prime}(,) B^{\prime \prime}(,) C^{\prime \prime}($,

Solution

Solution Steps

Step 1: Identify the coordinates of points A, B, and C

The coordinates of the points are given as:

A(1, 5)
B(6, 2)
C(8, 11)

Step 2: Translate 6 to the right and down 10

To translate a point 6 units to the right, add 6 to the x-coordinate. To translate a point 10 units down, subtract 10 from the y-coordinate.

For A(1, 5):
- New x-coordinate: 1 + 6 = 7
- New y-coordinate: 5 - 10 = -5
- A' = (7, -5)
For B(6, 2):
- New x-coordinate: 6 + 6 = 12
- New y-coordinate: 2 - 10 = -8
- B' = (12, -8)
For C(8, 11):
- New x-coordinate: 8 + 6 = 14
- New y-coordinate: 11 - 10 = 1
- C' = (14, 1)

Step 3: Translate 8 left and 2 up

To translate a point 8 units to the left, subtract 8 from the x-coordinate. To translate a point 2 units up, add 2 to the y-coordinate.

For A'(7, -5):
- New x-coordinate: 7 - 8 = -1
- New y-coordinate: -5 + 2 = -3
- A'' = (-1, -3)
For B'(12, -8):
- New x-coordinate: 12 - 8 = 4
- New y-coordinate: -8 + 2 = -6
- B'' = (4, -6)
For C'(14, 1):
- New x-coordinate: 14 - 8 = 6
- New y-coordinate: 1 + 2 = 3
- C'' = (6, 3)