Question

In which quadrant would (6, -1) be in if dilated at a scale factor of 5, centered at the origin?

Answer 1

Dilatioan formula for the original coordinates and the image is given below:

`(\text{ x , y ) }\to\text{ ( Scale factor}\cdot x\text{ , Scale factor}\cdot y\text{ )}`

The coordinates of the original point are given as follows:

`(\text{ 6 , -1 )}`

The scale factor for dilation is given as:

`\text{Scale Factor = 5}`

We will now use the dilation formula to determine the coordinates of image as follows:

`(\text{ 6 , - 1 ) }\to\text{ ( 5}\cdot6\text{ , 5}\cdot(-1)\text{ ) = ( 30 , -5 )}`

The image will lie in the quadrant defined by negative y-axis but positive x-axis! The quadrant would be:

`IV`