Question

What would be the coordinates of vertex B' of the parallelogram if it were dilated with respect to the origin using a magnitude of 3?
Coordinate A (-7,-5)
Coordinate B (-4,3)
Coordinate C (5,6)
Coordinate D (2,-2)

Answer 1

To find the coordinates of vertex B' of the parallelogram after dilation with respect to the origin using a magnitude of 3, we will apply the dilation transformation, which is defined as follows:

For a point \((x, y)\), the coordinates after dilation with respect to the origin by a factor of \(k\) are given by:
\[
(x', y') = (kx, ky)
\]

In this case, the coordinates of point B are given as:
\[
B(-4, 3)
\]
We want to dilate this point with a magnitude of \(k = 3\).

Using the dilation formula:
\[
B' = (3 \cdot -4, 3 \cdot 3)
\]
Calculating the new coordinates:
\[
B' = (-12, 9)
\]

Thus, the coordinates of vertex B' after dilation are:
\[
\boxed{(-12, 9)}
\]