Point A (12, 4) is the image of point A(3, 1) under a dilation with respect to the origin. What is the constant of dilation?

We conclude that the constant of dilation is: 4

Step-by-step explanation:

We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.

The coordinates of the image point can be determined by multiplying the coordinates of the original point by a certain scale factor.

Given the point A'(12, 4) is the image of A(3, 1).

It is clear that the image point A'(12, 4) is enlarged 4 times of the original point A(3, 1).

It means the image point A'(12, 4) is determined when the original point A(3, 1) is dilated by a scale factor of 4.

i.e.

A(3, 1) → A'(4(3), 4(1)) → A' (12, 4)

Therefore, the rule of dilation by a scale factor 4 is:

P(x, y) → P'(4x, 4y)

Hence, we conclude that the constant of dilation is: 4

$8

step-by-step explanation:

it is pretty much backwards.

you take the 4x2 multiply that, and that is = $8

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.