Which equation shows the relation between the vertices of a dilated figure and the vertices of the original figure when the original figure is dilated using a scale factor of 5?

Question

1. (x2,y2)=(x1+5,y1+5)
2. (x2,y2)=(5x1,5y1)
3. y2=x2+5,y1=x1+5
4. y2=5x2,y1=5x1

Answer 1

To show the relation between the vertices of a dilated figure and the vertices of the original figure using a scale factor, we need to understand that dilation involves multiplying the coordinates of the original figure by the scale factor.

In this case, the scale factor is 5. If \((x_1, y_1)\) are the coordinates of a point in the original figure, the coordinates \((x_2, y_2)\) of the corresponding point in the dilated figure can be expressed as:

\[ (x_2, y_2) = (5x_1, 5y_1) \]

Thus, the equation that correctly relates the vertices of the dilated figure to the original figure is:

\[ (x_2, y_2) = (5x_1, 5y_1) \]

This matches option 2 in your list.