Question

which equation shows the relationship between the vertices of the dilated figure and the vertices of the original figure. using a scale factor of 5

Answer 1

To show the relationship between the vertices of an original figure and its dilated figure using a scale factor of 5, we can use the concept of dilation in coordinate geometry.

Let's assume the original figure has vertices represented by the coordinates \((x, y)\). When we apply a dilation centered at the origin (0,0) with a scale factor of \(k\), the new coordinates \((x', y')\) of the dilated figure can be found using the following equations:

\[
x' = k \cdot x
\]
\[
y' = k \cdot y
\]

Since you have specified a scale factor of 5, we set \(k = 5\). Thus, the equations become:

\[
x' = 5 \cdot x
\]
\[
y' = 5 \cdot y
\]

These equations describe how the coordinates of the dilated figure (with vertices at \((x', y')\)) are related to the coordinates of the original figure (with vertices at \((x, y)\)) under a dilation with a scale factor of 5.

So, for any point \((x, y)\) on the original figure, the corresponding point on the dilated figure is given by:

\[
(x', y') = (5x, 5y)
\]