Question

which transformation does not preserve the size of a figure? a. dilation b. rotation c. reflection d. translation a parallelogram is reflected over the line y = x. what happens to the coordinates of the point (4, -2)?

Explanation:

Step1: Understand transformation types

Rotation, reflection and translation are rigid - motions. They preserve the size and shape of a figure. Dilation changes the size of a figure.

Step2: Analyze the options

• Option a: Dilation multiplies the distance of each point from the center of dilation by a scale factor. If the scale factor is not 1, the size of the figure changes.
• Option b: Rotation turns a figure around a fixed point. It does not change the size.
• Option c: Reflection flips a figure over a line. It does not change the size.
• Option d: Translation slides a figure. It does not change the size.

for second sub - question:

Step1: Recall reflection rule

When a point \((x,y)\) is reflected over the line \(y = x\), the transformation rule is \((x,y)\to(y,x)\)

Step2: Apply the rule

For the point \((4,-2)\), substituting \(x = 4\) and \(y=-2\) into the rule \((x,y)\to(y,x)\), we get \((-2,4)\)

Answer:

a. Dilation