Question

Translate Δ A B C 6 units horizontally. How are the values in the ordered pairs affected by the translation?

Answer 1

A graph of the image of the triangle ABC after a 6 units horizontal translation is shown in the diagram below. The x-coordinate of the ordered pairs are shifted by 6 units in both directions.

In Mathematics, a translation is a type of transformation that shifts every point of a geometric object in the same direction on the cartesian coordinate, as well as for the same distance.

In this exercise, we would apply a translation of 6 units to the left to triangle ABC (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 of 6 units to the right to triangle ABC (ΔABC), 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).

Answer 2

The x-coordinates are translated 6 units to the left or right while the y-coordinates are not affected.

Explanation:

The given triangle has vertices at A(-4,1), B(-2,1) and C(-2,4)

The transformation rule for a horizontal translation by k units is

`(x,y)\to (x\pm k,y)`

In this case we have k=6

`A(-4,1)\to A'(-4\pm6,1)`

`B(-2,1)\to B'(-2\pm6,1)`

`C(-2,4)\to C'(-2\pm6,4)`

Therefore the x-coordinates are translated 6 units to the left or right while the y-coordinates are not affected.

See attachment