geometry word problem

Question

Polygon ABCD is translated to create polygon A′B′C′D′. Point A is located at (1, 5), and point A′ is located at (-2, 3). Which expression defines the transformation of any point (x, y) to (x′, y′) on the polygons?

x′ = x − 3
y′ = y − 2


x′ = x − 2
y′ = y − 3


x′ = x − 1
y′ = y − 8


x = x′ + 3
y = y′ + 2

 

Answer 1

Dyani, since you are given answer choices, substitute your given values for x &y into each answer choice & see which one results in the x' & y' values that you were given in the original problem. Only one answer choice will match the given values.

 

FYI: If you are given this problem without answer choices, you need to see what change took place from x to x' & y to y'. For example: point A (2,4) and point A' (0,5). Let's first look at x & x'. X was 2 & x' is now 0. What happened? We subtracted 2. Therefore, x'=x-2. Let's do the same with y & y'. Y was 4 & y' is now 5. What happened? We added 1. Therefore, y'=y+1.

 

I hope this helps!

Answer 2

To get from A = (1, 5) = (x, y) to A' = (-2, 3) = (x', y'), subtract 3 from the x-coordinate of A and subtract 2 from the y-coordinate of A.

 

So, the transformation rule is: x' = x - 3

                                             y' = y - 2