Question

A dilation has center at origin. Which of the following is the image of the point p (7/4-5/2) for a scale factor of 1/7

Answer 1

c. 1/4, -5/14

Explanation:

i just did the test yourself and got it right

Answer 2

The image of the point p is
`p'((1)/(4),(-5)/(14))`.

Explanation:

The center of dilation is origin and the scale factor is
`(1)/(7)`.

The coordinates of point p are

`((7)/(4),(-5)/(2))`

If k is the scale factor and origin is the center of dilation, then

`(x,y)\rightarrow (kx,ky)`

Since the scale factor is
`(1)/(7)` and the origin is the center of dilation, therefore

`(x,y)\rightarrow ((1)/(7)x,(1)/(7)y)`

The coordinates of image of p are

`p((7)/(4),(-5)/(2))\rightarrow p'((1)/(7)* (7)/(4),(1)/(7)* (-5)/(2))`

`p((7)/(4),(-5)/(2))\rightarrow p'((1)/(4),(-5)/(14))`

Therefore the image of the point p is
`p'((1)/(4),(-5)/(14))`.