Question

mathematics diagnostic assessment
what is the rule for the transformation above?
a. (x,y)=( - 2x,-2y)
b. (x,y)=(2x,-2y)
c. (x,y)=(-2y,2x)
d. (x,y)=(-2x,2y)

Explanation:

Step1: Analyze transformation visually

Observe the position change of the shape in the coordinate - plane. Notice that the shape moves from the fourth quadrant to the second quadrant. The x - coordinate of each point on the shape changes sign (multiplies by - 1) and the y - coordinate changes sign (multiplies by - 1).
Let's assume a point \((x,y)\) on the original shape. After transformation, it becomes \((-x,-y)\).
For example, if we consider a vertex of the original shape with coordinates \((x,y)\), in the transformed shape, its coordinates should be such that the x - value and y - value are both negated.
If we take a general point \((x,y)\) and apply the transformation rule \((x,y)\to(-x,-y)\), we can check each option:

• Option A: \((x,y)\to(- 2x,-2y)\) is incorrect as it not only negates but also multiplies by 2.
• Option B: \((x,y)\to(2x,-2y)\) is incorrect as the x - coordinate is multiplied by 2 instead of being negated.
• Option C: \((x,y)\to(-2y,2x)\) is incorrect as it swaps and multiplies the coordinates in an incorrect way.
• Option D: \((x,y)\to(-x,-y)\) is correct as it simply negates both the x and y coordinates which is consistent with the visual transformation of the shape from the fourth quadrant to the second quadrant.

Answer:

D. \((x,y)=(-x,-y)\)