The image of P(-1, 5) under a translation is P'(5, 7). What is the preimage of P?

Could someone show me steps on how to do this problem, and the answer please?

Thank you.

The preimage is the original position before translation, or P(-1,5)

Well, well, well, let me put on my clown shoes and help you with this!

To find the preimage of point P(-1, 5), we need to undo the translation that was applied. Lucky for us, translations are pretty straightforward to undo!

Since the point moved from P(-1, 5) to P'(5, 7), it means it was shifted 6 units to the right and 2 units up.

To undo this translation, we just need to do the opposite. So, we shift P'(5, 7) 6 units to the left and 2 units down.

Therefore, the preimage of P'(5, 7) is P(-1 - 6, 5 - 2) = P(-7, 3).

So, the preimage of P is P(-7, 3).

I hope that helps! Just remember, when it comes to translations, it's all about going in the opposite direction. Keep clowning around with math!

To find the preimage of point P(-1, 5), we need to reverse the translation that was applied to get the image point P'(5, 7).

From the given information, we can observe that the translation vector is (5 - (-1), 7 - 5) = (6, 2). This means that every point is shifted 6 units to the right and 2 units up.

To find the preimage of P, we need to reverse this translation vector.

To shift 6 units to the left, we subtract 6 from the x-coordinate of P': 5 - 6 = -1.

To shift 2 units down, we subtract 2 from the y-coordinate of P': 7 - 2 = 5.

Therefore, the preimage of P'(5, 7) is P(-1, 5).

To find the preimage of a point after a translation, you need to reverse the translation process. In other words, you need to determine the original position of the point before it was translated.

In this problem, the translation took place from P(-1, 5) to P'(5, 7). The translation involves shifting the point horizontally and vertically by a certain amount.

To find the preimage, you need to figure out the amount by which the point was shifted horizontally and vertically.

To shift horizontally, you subtract the x-coordinate of P' from the x-coordinate of P:

Horizontal shift = x-coordinate of P - x-coordinate of P' = -1 - 5 = -6

To shift vertically, you subtract the y-coordinate of P' from the y-coordinate of P:

Vertical shift = y-coordinate of P - y-coordinate of P' = 5 - 7 = -2

Now, you can apply these shifts to the coordinates of P' to find the preimage:

x-coordinate of preimage = x-coordinate of P' + horizontal shift = 5 + (-6) = -1
y-coordinate of preimage = y-coordinate of P' + vertical shift = 7 + (-2) = 5

Therefore, the preimage of P is (-1, 5).