Question

What is the image point of (2,7) after the transformation r y=-x R270?

Answer 1

Answer:

0

Step-by-step explanation:|-2 - (-1)| =

|-2 + 1| =

| -1 | =

1.

 

So, we're one unit away from y = -1.  If we're one unit ABOVE y=-1, we need to move the point to be one unit BELOW it instead.  And if we're one unit BELOW y = -1, we need to move the point to be one unit ABOVE it.  

 

Since the point has a y-coordinate of -2, its BELOW the line y = -1, by 1 unit.  Now we change the y-coordinate so its instead ABOVE y = -1, by 1 unit:

 

(y-coordinate of reflection line) + (number of units above that line) =

-1 + 1 =

0.

 

Our new y-coordinate is 0, so the point is now at

(7, 0).

 

A more mechanical, but less intuitive approach is as follows:  

Let L = the y-coordinate of the line, and

P = the y-coordinate of the point.

The new y-coordinate is 2L - P.

In this case, L = -1, and P = -2.  So we have

2L - P =

2(-1) - (-2) =

-2 -(-2) =

0.