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

it’s C’(4,-2)

Explanation:

Answer 2

A. The x-coordinate of the ordered pairs are shifted by 6 units in both directions.

B. The y-coordinate of the ordered pairs are shifted by 3 units in both directions.

C. You can determine the coordinates of the vertices of a translated image without using a graph by either adding or subtracting from the x-values and y-values.

Part A.

In this exercise, we would apply a translation 6 units to the left to ΔABC, in order to determine the coordinates of its image as follows;

(x, y) → (x - 6, y)

A (-4, 1) → (-4 - 6, 1) = A' (-10, 1).

B (-1, 1) → (-1 - 6, 1) = B' (-7, 1).

C (-1, 4) → (-1 - 6, 4) = C' (-7, 4).

Next, we would apply a translation 6 units to the right to triangle ABC, in order to determine the coordinates of its image as follows;

(x, y) → (x + 6, y)

A (-4, 1) → (-4 + 6, 1) = A" (2, 1).

B (-1, 1) → (-1 + 6, 1) = B" (5, 1).

C (-1, 4) → (-1 + 6, 4) = C" (5, 4).

Part B.

By applying a vertical translation 3 units up and down to triangle ABC, the coordinates of its image are as follows;

(x, y) → (x, y + 3)

A (-4, 1) → (-4, 1 + 3) = A' (-4, 4).

B (-1, 1) → (-1, 1 + 3) = B' (-1, 4).

C (-1, 4) → (-1, 4 + 3) = C' (-1, 7).

(x, y) → (x, y - 3)

A (-4, 1) → (-4, 1 - 3) = A' (-4, -2).

B (-1, 1) → (-1, 1 - 3) = B' (-1, -2).

C (-1, 4) → (-1, 4 - 3) = C' (-1, 1).

Part C.

You can determine the coordinates of the vertices of a translated image without using a graph by either adding or subtracting from the x-coordinates and y-coordinates of the pre-image.

Missing information:

The question is incomplete and the missing figure is shown in the attached picture.