Question

Rigid Transformations:Question 1Circle P has center (-9, 3) and radius 3. Circle P' is formedby shifting circle P to the right 4 units and reflecting aboutthe line y = x. What is the coordinate of the center of circleP'?Select one:O(-13, 3)O(-5,3)O(3.-13)(3-5)

Answer 1

To shift the coordinates in a cartesian plane we have to remember that a translation can be described as:

$(x,y)\rightarrow(x+a,y+b)$

where a and b is the amount we would like to translate in the horizontal and vertical direction, respectively.

In this case we would like to translate the center to the right four units, then a=4. Since we don't wish to translate it in the vertical direction then b=0. Then, the center, after the tanslation is

$P^{}=(-9+4,3)=(-5,3)$

Now, if we want to reflect about the line y=x we have to remember that the rule describing it is

$(x,y)\rightarrow(y,x)$

Then the point P' is

$P^{\prime}=(3,-5)$

Therefore the center of the circle after the transformations given is (3,-5)