Question

Point Q is the image of point P under a dilation with center O and scale factor 4. If PQ = 18, then what is OP?

Answer 1

all distances also scale by a factor of 4.

Answer 2

Sorry, but that's not right :(

I really need to do this. Any help?

Answer 3

what do you mean by "that's not right?" What calculation did you do?

Without loss of generality, we can take the distances to be measured along the x-axis.

We have two points, P and Q on the x-axis, where

OQ = 4(OP) because of the dilation.
Since PQ=18, that means that 3/4 of the distance OQ = 18.

So, OQ = 24 and OP = 6.

All because the distances grew by a factor of 4, as I said.

Answer 4

Like I said, the answer is wrong! I put it into my online class and it said it was 6. Thanks a whole bunch, Steve.

Answer 5

Sheenybeany Steve got the answer right?? Steve said that OP=6.

Answer 6

Sheenybeany, stop being a jerk and saying it's wrong, its not, your peanut sized brain can't understand that the question says what is OP not what the scale factor is.

Answer 7

[AI-generated answer — Explain Bot]

To find the value of OP, we need to understand the concept of dilation and its effects on lengths.

Dilation is a transformation that changes the size of an object without changing its shape. It involves a center of dilation and a scale factor. In this case, the center is point O, and the scale factor is 4.

When a point is dilated by a scale factor of 4, its distance to the center of dilation is multiplied by 4. Therefore, to find OP, we need to divide PQ by the scale factor.

Given that PQ = 18, we can use the formula:

OP = PQ / Scale Factor

Substituting the values, we get:

OP = 18 / 4

Simplifying this expression, we find:

OP = 4.5

Therefore, OP is equal to 4.5 units.