Question

What are the coordinates of the image of the point (1-, 2) under a dilation of 3 with the origin

Answer 1

Answer:

The image of the point (1, -2) under a dilation of 3 is (3, -6).

Step-by-step explanation:

Correct statement is:

What are the coordinates of the image of the point (1, -2) under a dilation of 3 with the origin.

From Linear Algebra we get that dilation of a point with respect to another point is represented by:

$\vec P' = \vec R + r\cdot (\vec P-\vec R)$ (Eq. 1)

Where:

$\vec R$ - Reference point with respect to origin, dimensionless.

$\vec P$ - Original point with respect to origin, dimensionless.

$r$ - Dilation factor, dimensionless.

If we know that $\vec R = (0,0)$, $\vec P = (1, -2)$ and $r = 3$, then the coordinates of the image of the original point is:

$\vec P' = (0,0) +3\cdot [(1,-2)-(0,0)]$

$\vec P' = (0,0) + 3\cdot (1,-2)$

$\vec P' = (3,-6)$

The image of the point (1, -2) under a dilation of 3 is (3, -6).