Question

Point A has coordinates (3,4). After a translation 4 units left, a reflection across the x-axis, and a translation 2 units down, what are the coordinates of the image? Write your coordinates with a comma and no spaces inside parenthesis, for example (1,2).

Answer 1

If a point, (x, y) is translated c units to the left, the new coordinate would be

(x - c, y)

Given that point A with coordinates, (3, 4) is translated 4 units left, the new coordinate would be

(3 - 4, 4)

= (- 1, 4)

If a point, (x, y) is reflected across the x-axis, the sign of the x coordinate remains unchanged while the sign of the y coordinate would change. This gives us (x, - y). Thus, if (- 1, 4) is reflected across the x-axis, the new point would be

(- 1, - 4)

If a point, (x, y) is translated c units down, the new point would be (x, y - c)

Thus, if (- 1, - 4) is translated 2 units down, the new point would be (- 1, - 4 - 2)

= (- 1, - 6)

The final coordinate is

(- 1, - 6)