Question

If the triangle were reflected across the x-axis, then translated four units to the left,

what would be the value of the x-coordinate of point B?

Answer 1

After the point B is reflected across the x-axis and then translated four units to the left, the value of the x-coordinate of point B would become -7.00 m.

Step-by-step explanation:

If the triangle were reflected across the x-axis, then translated four units to the left, the position of a point B on the triangle would be affected in two distinct steps. First, reflecting across the x-axis will invert the y-coordinate of point B while leaving the x-coordinate unaffected. Then, translating the triangle four units to the left would subtract four from the x-coordinate of point B. For example, if B had an initial position of B(x, y), after the reflection, it would be at B(x, -y), and after the translation, it would be at B'(x-4, -y).

To illustrate this with values, if point B is originally located at B(-3.00 m, 3.00 m), reflecting across the x-axis would give us B(-3.00 m, -3.00 m). Then, translating four units to the left would result in the point being located at B'(-7.00 m, -3.00 m). Therefore, the value of the x-coordinate of point B after these transformations would be -7.00 m.

Answer 2

When the triangle is reflected across the x-axis, then point B would be (6, -6), but when it's also translated four units to the left, it will be (2, -6).

When you reflect something across an axis, then a point you recall will have the x or y value have the opposite sign (i.e. 6 would become -6 across the x-axis and vice versa).

When you translate something across the graph, you are adding to the x value when shifting to the right, subtracting from the x value when shifting to the left, adding to the y value when shifting upward, and subtracting from the y value when shifting downward.

∴, B = (2, -6).