Question

a triangle is dilated with a scale factor of 0.5. which of the following is true about the image?the image is rotated 180°.the image is congruent to the original.the image is flipped over the x - axis.the image is similar but smaller than the original.question 5two angles are vertical and one measures 42°. what is the measure of the other?48°90°138°

Explanation:

Step1: Properties of dilation

Dilation is a transformation that changes the size of a figure but not its shape. If the scale factor is between \(0\) and \(1\) (here \(0.5\)), the image is smaller than the original. Also, similar figures have the same shape (corresponding angles are equal) and their sides are in proportion.

Step2: Analyze each option

• Rotation (\(180^{\circ}\)) is a different transformation (not related to dilation).
• Congruent figures have the same size (scale factor \(1\)), but here scale factor is \(0.5\).
• Flipping (reflection) over the \(x -\)axis is a different transformation (not related to dilation).
• Since dilation with scale factor \(0.5\) changes size (makes it smaller) and keeps shape (similarity).

Step3: Properties of vertical angles

Vertical angles are equal. If one vertical angle measures \(42^{\circ}\), then the other vertical angle also measures \(42^{\circ}\). But since there is no \(42^{\circ}\) option, there might be a mis - understanding. Wait, no, let's check again. Wait, no, for the second question:
Vertical angles are formed when two lines intersect. They are opposite each other and are equal in measure.

Answer:

For the first question: The image is similar but smaller than the original.
For the second question: None of the given options (\(48^{\circ},90^{\circ},138^{\circ}\)) are correct. The measure of the other vertical angle should be \(42^{\circ}\). But if we assume it's a wrong - option - set case (maybe a typo in the problem), but based on the property of vertical angles (equality), if we have to choose from the given options, there is an error. But if we consider supplementary angles (a wrong approach but just to fit the options), if it was a linear - pair - like wrong assumption (but vertical angles are not supplementary unless they are right angles). Wait, no, vertical angles are equal. So the answer for the second question is that there is an error in the options as the measure should be \(42^{\circ}\). But if we assume it's a mis - labeled problem (maybe adjacent angles instead of vertical, but no, the question says vertical). So strictly by vertical - angle property: no correct option. But if forced (which is wrong), but if we consider the first problem: The image is similar but smaller than the original.