Question

points a and b represent points on a safety pin. points a and b represent points on the image of the safety pin after a dilation centered at the origin. what is the relationship between the coordinates of corresponding points? coordinates of corresponding points are opposites. coordinates of corresponding points are always equal. coordinates of corresponding points are proportional.

Explanation:

Step1: Calculate the ratio of \(x\) - coordinates

For point \(A(4,4)\) and \(A'(6,6)\), the ratio of \(x\) - coordinates is \(\frac{6}{4}=\frac{3}{2}\). For point \(B(6,2)\) and \(B'(9,3)\), the ratio of \(x\) - coordinates is \(\frac{9}{6}=\frac{3}{2}\).

Step2: Calculate the ratio of \(y\) - coordinates

For point \(A(4,4)\) and \(A'(6,6)\), the ratio of \(y\) - coordinates is \(\frac{6}{4}=\frac{3}{2}\). For point \(B(6,2)\) and \(B'(9,3)\), the ratio of \(y\) - coordinates is \(\frac{3}{2}\).

Since the ratios of the \(x\) - coordinates and \(y\) - coordinates of corresponding points (\(A\) and \(A'\), \(B\) and \(B'\)) are equal, the coordinates of corresponding points are proportional.

Answer:

Coordinates of corresponding points are proportional.