Question

After applying a translation vector to rectangle ABDC , the coordinates of A′ are (−6,8) . What are the coordinates of B′ ?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the coordinates of B', we need to know the translation vector that was applied to rectangle ABDC.

The translation vector represents the change in position of a point after the translation. It consists of two components: the horizontal component (x-direction) and the vertical component (y-direction).

Let's assume the translation vector is represented by the components (a, b), where a is the horizontal component and b is the vertical component.

If the coordinates of A are (x1, y1) and the coordinates of A' are (x1', y1'), then the coordinates of any other point B on the rectangle ABDC can be found as follows:

x2' = x1' + (x2 - x1)
y2' = y1' + (y2 - y1)

Given that the coordinates of A are (x1, y1) = (0, 0) and the coordinates of A' are (x1', y1') = (-6, 8), we can substitute these values into the equations:

x2' = -6 + (x2 - 0)
y2' = 8 + (y2 - 0)

Since the rectangle is symmetric along the x-axis and y-axis, the change in position of B relative to A in the x-direction will be the same as the change in position of A' relative to A. Therefore, the horizontal component of the translation vector can be calculated as:

a = x1' - x1 = -6 - 0 = -6

Substituting this value into the equation for x2', we get:

x2' = -6 + (x2 - 0)

To find the y-coordinate of B', we need to know the vertical component of the translation vector. Without this information, we cannot determine the exact coordinates of B'.